diff --git a/data_2D-Euler-Adaptive.txt b/data_2D-Euler-Adaptive.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b5507972cc4c84bb42bfd91abbb8d01903c9c654
--- /dev/null
+++ b/data_2D-Euler-Adaptive.txt
@@ -0,0 +1,117 @@
+h | exact | result | error | error_estimated
+0.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 0.00000 , 0.00000 | 0.49050
+0.14515 | 0.14515 , 0.24850 , 1.00000 , 2.42394 | 0.04515 , 0.04515 , 1.00000 , 1.44294 | 0.10000 , 0.20334 , 0.00000 , 0.98100 | 0.22147
+0.17549 | 0.17549 , 0.32656 , 1.00000 , 2.72158 | 0.07549 , 0.08893 , 1.00000 , 1.74058 | 0.10000 , 0.23762 , 0.00000 , 0.98100 | 0.14882
+0.20036 | 0.20036 , 0.39728 , 1.00000 , 2.96557 | 0.10036 , 0.13222 , 1.00000 , 1.98457 | 0.10000 , 0.26506 , 0.00000 , 0.98100 | 0.12199
+0.22288 | 0.22288 , 0.46654 , 1.00000 , 3.18647 | 0.12288 , 0.17691 , 1.00000 , 2.20547 | 0.10000 , 0.28963 , 0.00000 , 0.98100 | 0.11045
+0.24431 | 0.24431 , 0.53707 , 1.00000 , 3.39666 | 0.14431 , 0.22416 , 1.00000 , 2.41566 | 0.10000 , 0.31290 , 0.00000 , 0.98100 | 0.10510
+0.26521 | 0.26521 , 0.61020 , 1.00000 , 3.60169 | 0.16521 , 0.27465 , 1.00000 , 2.62069 | 0.10000 , 0.33555 , 0.00000 , 0.98100 | 0.10252
+0.28585 | 0.28585 , 0.68664 , 1.00000 , 3.80419 | 0.18585 , 0.32875 , 1.00000 , 2.82319 | 0.10000 , 0.35789 , 0.00000 , 0.98100 | 0.10125
+0.30636 | 0.30636 , 0.76674 , 1.00000 , 4.00543 | 0.20636 , 0.38667 , 1.00000 , 3.02443 | 0.10000 , 0.38008 , 0.00000 , 0.98100 | 0.10062
+0.32682 | 0.32682 , 0.85071 , 1.00000 , 4.20606 | 0.22682 , 0.44852 , 1.00000 , 3.22506 | 0.10000 , 0.40219 , 0.00000 , 0.98100 | 0.10031
+0.34723 | 0.34723 , 0.93864 , 1.00000 , 4.40637 | 0.24723 , 0.51437 , 1.00000 , 3.42537 | 0.10000 , 0.42427 , 0.00000 , 0.98100 | 0.10016
+0.36764 | 0.36764 , 1.03058 , 1.00000 , 4.60652 | 0.26764 , 0.58426 , 1.00000 , 3.62552 | 0.10000 , 0.44633 , 0.00000 , 0.98100 | 0.10008
+0.38803 | 0.38803 , 1.12658 , 1.00000 , 4.80660 | 0.28803 , 0.65820 , 1.00000 , 3.82560 | 0.10000 , 0.46837 , 0.00000 , 0.98100 | 0.10004
+0.40842 | 0.40842 , 1.22663 , 1.00000 , 5.00664 | 0.30842 , 0.73621 , 1.00000 , 4.02564 | 0.10000 , 0.49042 , 0.00000 , 0.98100 | 0.10002
+0.42881 | 0.42881 , 1.33075 , 1.00000 , 5.20666 | 0.32881 , 0.81829 , 1.00000 , 4.22566 | 0.10000 , 0.51246 , 0.00000 , 0.98100 | 0.10001
+0.44920 | 0.44920 , 1.43894 , 1.00000 , 5.40667 | 0.34920 , 0.90445 , 1.00000 , 4.42567 | 0.10000 , 0.53450 , 0.00000 , 0.98100 | 0.10000
+0.46959 | 0.46959 , 1.55121 , 1.00000 , 5.60667 | 0.36959 , 0.99468 , 1.00000 , 4.62567 | 0.10000 , 0.55654 , 0.00000 , 0.98100 | 0.10000
+0.48998 | 0.48998 , 1.66756 , 1.00000 , 5.80668 | 0.38998 , 1.08898 , 1.00000 , 4.82568 | 0.10000 , 0.57858 , 0.00000 , 0.98100 | 0.10000
+0.51036 | 0.51036 , 1.78798 , 1.00000 , 6.00668 | 0.41036 , 1.18736 , 1.00000 , 5.02568 | 0.10000 , 0.60062 , 0.00000 , 0.98100 | 0.10000
+0.53075 | 0.53075 , 1.91248 , 1.00000 , 6.20668 | 0.43075 , 1.28983 , 1.00000 , 5.22568 | 0.10000 , 0.62265 , 0.00000 , 0.98100 | 0.10000
+0.55114 | 0.55114 , 2.04106 , 1.00000 , 6.40668 | 0.45114 , 1.39636 , 1.00000 , 5.42568 | 0.10000 , 0.64469 , 0.00000 , 0.98100 | 0.10000
+0.57153 | 0.57153 , 2.17371 , 1.00000 , 6.60668 | 0.47153 , 1.50698 , 1.00000 , 5.62568 | 0.10000 , 0.66673 , 0.00000 , 0.98100 | 0.10000
+0.59191 | 0.59191 , 2.31044 , 1.00000 , 6.80668 | 0.49191 , 1.62167 , 1.00000 , 5.82568 | 0.10000 , 0.68877 , 0.00000 , 0.98100 | 0.10000
+0.61230 | 0.61230 , 2.45125 , 1.00000 , 7.00668 | 0.51230 , 1.74044 , 1.00000 , 6.02568 | 0.10000 , 0.71081 , 0.00000 , 0.98100 | 0.10000
+0.63269 | 0.63269 , 2.59614 , 1.00000 , 7.20668 | 0.53269 , 1.86329 , 1.00000 , 6.22568 | 0.10000 , 0.73285 , 0.00000 , 0.98100 | 0.10000
+0.65308 | 0.65308 , 2.74510 , 1.00000 , 7.40668 | 0.55308 , 1.99021 , 1.00000 , 6.42568 | 0.10000 , 0.75489 , 0.00000 , 0.98100 | 0.10000
+0.67346 | 0.67346 , 2.89814 , 1.00000 , 7.60668 | 0.57346 , 2.12122 , 1.00000 , 6.62568 | 0.10000 , 0.77693 , 0.00000 , 0.98100 | 0.10000
+0.69385 | 0.69385 , 3.05526 , 1.00000 , 7.80668 | 0.59385 , 2.25630 , 1.00000 , 6.82568 | 0.10000 , 0.79896 , 0.00000 , 0.98100 | 0.10000
+0.71424 | 0.71424 , 3.21646 , 1.00000 , 8.00668 | 0.61424 , 2.39545 , 1.00000 , 7.02568 | 0.10000 , 0.82100 , 0.00000 , 0.98100 | 0.10000
+0.73463 | 0.73463 , 3.38173 , 1.00000 , 8.20668 | 0.63463 , 2.53869 , 1.00000 , 7.22568 | 0.10000 , 0.84304 , 0.00000 , 0.98100 | 0.10000
+0.75501 | 0.75501 , 3.55108 , 1.00000 , 8.40668 | 0.65501 , 2.68600 , 1.00000 , 7.42568 | 0.10000 , 0.86508 , 0.00000 , 0.98100 | 0.10000
+0.77540 | 0.77540 , 3.72451 , 1.00000 , 8.60668 | 0.67540 , 2.83739 , 1.00000 , 7.62568 | 0.10000 , 0.88712 , 0.00000 , 0.98100 | 0.10000
+0.79579 | 0.79579 , 3.90202 , 1.00000 , 8.80668 | 0.69579 , 2.99286 , 1.00000 , 7.82568 | 0.10000 , 0.90916 , 0.00000 , 0.98100 | 0.10000
+0.81618 | 0.81618 , 4.08360 , 1.00000 , 9.00668 | 0.71618 , 3.15240 , 1.00000 , 8.02568 | 0.10000 , 0.93120 , 0.00000 , 0.98100 | 0.10000
+0.83656 | 0.83656 , 4.26926 , 1.00000 , 9.20668 | 0.73656 , 3.31603 , 1.00000 , 8.22568 | 0.10000 , 0.95324 , 0.00000 , 0.98100 | 0.10000
+0.85695 | 0.85695 , 4.45900 , 1.00000 , 9.40668 | 0.75695 , 3.48373 , 1.00000 , 8.42568 | 0.10000 , 0.97527 , 0.00000 , 0.98100 | 0.10000
+0.87734 | 0.87734 , 4.65282 , 1.00000 , 9.60668 | 0.77734 , 3.65550 , 1.00000 , 8.62568 | 0.10000 , 0.99731 , 0.00000 , 0.98100 | 0.10000
+0.89772 | 0.89772 , 4.85071 , 1.00000 , 9.80668 | 0.79772 , 3.83136 , 1.00000 , 8.82568 | 0.10000 , 1.01935 , 0.00000 , 0.98100 | 0.10000
+0.91811 | 0.91811 , 5.05268 , 1.00000 , 10.00668 | 0.81811 , 4.01129 , 1.00000 , 9.02568 | 0.10000 , 1.04139 , 0.00000 , 0.98100 | 0.10000
+0.93850 | 0.93850 , 5.25873 , 1.00000 , 10.20668 | 0.83850 , 4.19530 , 1.00000 , 9.22568 | 0.10000 , 1.06343 , 0.00000 , 0.98100 | 0.10000
+0.95889 | 0.95889 , 5.46886 , 1.00000 , 10.40668 | 0.85889 , 4.38339 , 1.00000 , 9.42568 | 0.10000 , 1.08547 , 0.00000 , 0.98100 | 0.10000
+0.97927 | 0.97927 , 5.68306 , 1.00000 , 10.60668 | 0.87927 , 4.57555 , 1.00000 , 9.62568 | 0.10000 , 1.10751 , 0.00000 , 0.98100 | 0.10000
+0.99966 | 0.99966 , 5.90134 , 1.00000 , 10.80668 | 0.89966 , 4.77180 , 1.00000 , 9.82568 | 0.10000 , 1.12955 , 0.00000 , 0.98100 | 0.10016
+1.02003 | 1.02003 , 6.12352 , 1.00000 , 11.00652 | 0.92003 , 4.97196 , 1.00000 , 10.02552 | 0.10000 , 1.15156 , 0.00000 , 0.98100 | 0.10212
+1.04019 | 1.04019 , 6.34739 , 1.00000 , 11.20428 | 0.94019 , 5.17406 , 1.00000 , 10.22328 | 0.10000 , 1.17333 , 0.00000 , 0.98100 | 0.10305
+1.06005 | 1.06005 , 6.57183 , 1.00000 , 11.39909 | 0.96005 , 5.37708 , 1.00000 , 10.41809 | 0.10000 , 1.19475 , 0.00000 , 0.98100 | 0.10345
+1.07958 | 1.07958 , 6.79627 , 1.00000 , 11.59064 | 0.97958 , 5.58050 , 1.00000 , 10.60964 | 0.10000 , 1.21577 , 0.00000 , 0.98100 | 0.10358
+1.09876 | 1.09876 , 7.02045 , 1.00000 , 11.77884 | 0.99876 , 5.78405 , 1.00000 , 10.79784 | 0.10000 , 1.23640 , 0.00000 , 0.98100 | 0.10358
+1.11761 | 1.11761 , 7.24423 , 1.00000 , 11.96377 | 1.01761 , 5.98759 , 1.00000 , 10.98277 | 0.10000 , 1.25664 , 0.00000 , 0.98100 | 0.10352
+1.13614 | 1.13614 , 7.46757 , 1.00000 , 12.14553 | 1.03614 , 6.19108 , 1.00000 , 11.16453 | 0.10000 , 1.27650 , 0.00000 , 0.98100 | 0.10343
+1.15436 | 1.15436 , 7.69047 , 1.00000 , 12.32425 | 1.05436 , 6.39448 , 1.00000 , 11.34325 | 0.10000 , 1.29600 , 0.00000 , 0.98100 | 0.10333
+1.17228 | 1.17228 , 7.91293 , 1.00000 , 12.50007 | 1.07228 , 6.59778 , 1.00000 , 11.51907 | 0.10000 , 1.31515 , 0.00000 , 0.98100 | 0.10323
+1.18992 | 1.18992 , 8.13496 , 1.00000 , 12.67312 | 1.08992 , 6.80098 , 1.00000 , 11.69212 | 0.10000 , 1.33398 , 0.00000 , 0.98100 | 0.10313
+1.20729 | 1.20729 , 8.35658 , 1.00000 , 12.84353 | 1.10729 , 7.00408 , 1.00000 , 11.86253 | 0.10000 , 1.35251 , 0.00000 , 0.98100 | 0.10303
+1.22440 | 1.22440 , 8.57782 , 1.00000 , 13.01141 | 1.12440 , 7.20709 , 1.00000 , 12.03041 | 0.10000 , 1.37073 , 0.00000 , 0.98100 | 0.10294
+1.24127 | 1.24127 , 8.79868 , 1.00000 , 13.17688 | 1.14127 , 7.41001 , 1.00000 , 12.19588 | 0.10000 , 1.38867 , 0.00000 , 0.98100 | 0.10286
+1.25790 | 1.25790 , 9.01919 , 1.00000 , 13.34003 | 1.15790 , 7.61284 , 1.00000 , 12.35903 | 0.10000 , 1.40634 , 0.00000 , 0.98100 | 0.10277
+1.27431 | 1.27431 , 9.23936 , 1.00000 , 13.50097 | 1.17431 , 7.81560 , 1.00000 , 12.51997 | 0.10000 , 1.42376 , 0.00000 , 0.98100 | 0.10270
+1.29050 | 1.29050 , 9.45920 , 1.00000 , 13.65978 | 1.19050 , 8.01828 , 1.00000 , 12.67878 | 0.10000 , 1.44092 , 0.00000 , 0.98100 | 0.10263
+1.30648 | 1.30648 , 9.67874 , 1.00000 , 13.81654 | 1.20648 , 8.22089 , 1.00000 , 12.83554 | 0.10000 , 1.45785 , 0.00000 , 0.98100 | 0.10256
+1.32226 | 1.32226 , 9.89798 , 1.00000 , 13.97134 | 1.22226 , 8.42343 , 1.00000 , 12.99034 | 0.10000 , 1.47456 , 0.00000 , 0.98100 | 0.10249
+1.33784 | 1.33784 , 10.11694 , 1.00000 , 14.12425 | 1.23784 , 8.62590 , 1.00000 , 13.14325 | 0.10000 , 1.49104 , 0.00000 , 0.98100 | 0.10243
+1.35324 | 1.35324 , 10.33563 , 1.00000 , 14.27533 | 1.25324 , 8.82832 , 1.00000 , 13.29433 | 0.10000 , 1.50731 , 0.00000 , 0.98100 | 0.10237
+1.36847 | 1.36847 , 10.55405 , 1.00000 , 14.42465 | 1.26847 , 9.03067 , 1.00000 , 13.44365 | 0.10000 , 1.52338 , 0.00000 , 0.98100 | 0.10231
+1.38351 | 1.38351 , 10.77223 , 1.00000 , 14.57227 | 1.28351 , 9.23298 , 1.00000 , 13.59127 | 0.10000 , 1.53925 , 0.00000 , 0.98100 | 0.10226
+1.39839 | 1.39839 , 10.99016 , 1.00000 , 14.71825 | 1.29839 , 9.43523 , 1.00000 , 13.73725 | 0.10000 , 1.55493 , 0.00000 , 0.98100 | 0.10221
+1.41311 | 1.41311 , 11.20786 , 1.00000 , 14.86265 | 1.31311 , 9.63742 , 1.00000 , 13.88165 | 0.10000 , 1.57044 , 0.00000 , 0.98100 | 0.10216
+1.42768 | 1.42768 , 11.42534 , 1.00000 , 15.00550 | 1.32768 , 9.83957 , 1.00000 , 14.02450 | 0.10000 , 1.58576 , 0.00000 , 0.98100 | 0.10212
+1.44209 | 1.44209 , 11.64260 , 1.00000 , 15.14687 | 1.34209 , 10.04168 , 1.00000 , 14.16587 | 0.10000 , 1.60092 , 0.00000 , 0.98100 | 0.10207
+1.45635 | 1.45635 , 11.85965 , 1.00000 , 15.28680 | 1.35635 , 10.24374 , 1.00000 , 14.30580 | 0.10000 , 1.61591 , 0.00000 , 0.98100 | 0.10203
+1.47047 | 1.47047 , 12.07650 , 1.00000 , 15.42533 | 1.37047 , 10.44576 , 1.00000 , 14.44433 | 0.10000 , 1.63074 , 0.00000 , 0.98100 | 0.10199
+1.48446 | 1.48446 , 12.29315 , 1.00000 , 15.56251 | 1.38446 , 10.64773 , 1.00000 , 14.58151 | 0.10000 , 1.64542 , 0.00000 , 0.98100 | 0.10195
+1.49830 | 1.49830 , 12.50962 , 1.00000 , 15.69836 | 1.39830 , 10.84967 , 1.00000 , 14.71736 | 0.10000 , 1.65994 , 0.00000 , 0.98100 | 0.10191
+1.51202 | 1.51202 , 12.72590 , 1.00000 , 15.83294 | 1.41202 , 11.05157 , 1.00000 , 14.85194 | 0.10000 , 1.67432 , 0.00000 , 0.98100 | 0.10187
+1.52561 | 1.52561 , 12.94200 , 1.00000 , 15.96628 | 1.42561 , 11.25344 , 1.00000 , 14.98528 | 0.10000 , 1.68856 , 0.00000 , 0.98100 | 0.10184
+1.53908 | 1.53908 , 13.15793 , 1.00000 , 16.09841 | 1.43908 , 11.45527 , 1.00000 , 15.11741 | 0.10000 , 1.70267 , 0.00000 , 0.98100 | 0.10180
+1.55243 | 1.55243 , 13.37370 , 1.00000 , 16.22936 | 1.45243 , 11.65706 , 1.00000 , 15.24836 | 0.10000 , 1.71664 , 0.00000 , 0.98100 | 0.10177
+1.56566 | 1.56566 , 13.58930 , 1.00000 , 16.35916 | 1.46566 , 11.85883 , 1.00000 , 15.37816 | 0.10000 , 1.73047 , 0.00000 , 0.98100 | 0.10174
+1.57878 | 1.57878 , 13.80475 , 1.00000 , 16.48785 | 1.47878 , 12.06056 , 1.00000 , 15.50685 | 0.10000 , 1.74419 , 0.00000 , 0.98100 | 0.10171
+1.59179 | 1.59179 , 14.02004 , 1.00000 , 16.61545 | 1.49179 , 12.26227 , 1.00000 , 15.63445 | 0.10000 , 1.75778 , 0.00000 , 0.98100 | 0.10168
+1.60469 | 1.60469 , 14.23519 , 1.00000 , 16.74200 | 1.50469 , 12.46394 , 1.00000 , 15.76100 | 0.10000 , 1.77125 , 0.00000 , 0.98100 | 0.10165
+1.61748 | 1.61748 , 14.45019 , 1.00000 , 16.86751 | 1.51748 , 12.66559 , 1.00000 , 15.88651 | 0.10000 , 1.78460 , 0.00000 , 0.98100 | 0.10163
+1.63017 | 1.63017 , 14.66505 , 1.00000 , 16.99201 | 1.53017 , 12.86721 , 1.00000 , 16.01101 | 0.10000 , 1.79784 , 0.00000 , 0.98100 | 0.10160
+1.64276 | 1.64276 , 14.87977 , 1.00000 , 17.11552 | 1.54276 , 13.06880 , 1.00000 , 16.13452 | 0.10000 , 1.81097 , 0.00000 , 0.98100 | 0.10157
+1.65526 | 1.65526 , 15.09436 , 1.00000 , 17.23808 | 1.55526 , 13.27037 , 1.00000 , 16.25708 | 0.10000 , 1.82399 , 0.00000 , 0.98100 | 0.10155
+1.66766 | 1.66766 , 15.30882 , 1.00000 , 17.35970 | 1.56766 , 13.47191 , 1.00000 , 16.37870 | 0.10000 , 1.83691 , 0.00000 , 0.98100 | 0.10153
+1.67996 | 1.67996 , 15.52315 , 1.00000 , 17.48040 | 1.57996 , 13.67343 , 1.00000 , 16.49940 | 0.10000 , 1.84972 , 0.00000 , 0.98100 | 0.10150
+1.69217 | 1.69217 , 15.73736 , 1.00000 , 17.60020 | 1.59217 , 13.87493 , 1.00000 , 16.61920 | 0.10000 , 1.86243 , 0.00000 , 0.98100 | 0.10148
+1.70429 | 1.70429 , 15.95145 , 1.00000 , 17.71913 | 1.60429 , 14.07640 , 1.00000 , 16.73813 | 0.10000 , 1.87505 , 0.00000 , 0.98100 | 0.10146
+1.71633 | 1.71633 , 16.16542 , 1.00000 , 17.83720 | 1.61633 , 14.27786 , 1.00000 , 16.85620 | 0.10000 , 1.88756 , 0.00000 , 0.98100 | 0.10144
+1.72828 | 1.72828 , 16.37928 , 1.00000 , 17.95443 | 1.62828 , 14.47929 , 1.00000 , 16.97343 | 0.10000 , 1.89999 , 0.00000 , 0.98100 | 0.10142
+1.74015 | 1.74015 , 16.59302 , 1.00000 , 18.07083 | 1.64015 , 14.68070 , 1.00000 , 17.08983 | 0.10000 , 1.91232 , 0.00000 , 0.98100 | 0.10140
+1.75193 | 1.75193 , 16.80665 , 1.00000 , 18.18644 | 1.65193 , 14.88209 , 1.00000 , 17.20544 | 0.10000 , 1.92456 , 0.00000 , 0.98100 | 0.10138
+1.76363 | 1.76363 , 17.02018 , 1.00000 , 18.30125 | 1.66363 , 15.08346 , 1.00000 , 17.32025 | 0.10000 , 1.93671 , 0.00000 , 0.98100 | 0.10136
+1.77526 | 1.77526 , 17.23360 , 1.00000 , 18.41530 | 1.67526 , 15.28482 , 1.00000 , 17.43430 | 0.10000 , 1.94878 , 0.00000 , 0.98100 | 0.10134
+1.78681 | 1.78681 , 17.44692 , 1.00000 , 18.52859 | 1.68681 , 15.48615 , 1.00000 , 17.54759 | 0.10000 , 1.96076 , 0.00000 , 0.98100 | 0.10132
+1.79828 | 1.79828 , 17.66013 , 1.00000 , 18.64113 | 1.69828 , 15.68747 , 1.00000 , 17.66013 | 0.10000 , 1.97266 , 0.00000 , 0.98100 | 0.10130
+1.80968 | 1.80968 , 17.87325 , 1.00000 , 18.75295 | 1.70968 , 15.88877 , 1.00000 , 17.77195 | 0.10000 , 1.98448 , 0.00000 , 0.98100 | 0.10129
+1.82101 | 1.82101 , 18.08628 , 1.00000 , 18.86406 | 1.72101 , 16.09005 , 1.00000 , 17.88306 | 0.10000 , 1.99622 , 0.00000 , 0.98100 | 0.10127
+1.83226 | 1.83226 , 18.29921 , 1.00000 , 18.97447 | 1.73226 , 16.29132 , 1.00000 , 17.99347 | 0.10000 , 2.00789 , 0.00000 , 0.98100 | 0.10125
+1.84344 | 1.84344 , 18.51204 , 1.00000 , 19.08419 | 1.74344 , 16.49257 , 1.00000 , 18.10319 | 0.10000 , 2.01947 , 0.00000 , 0.98100 | 0.10124
+1.85456 | 1.85456 , 18.72479 , 1.00000 , 19.19324 | 1.75456 , 16.69381 , 1.00000 , 18.21224 | 0.10000 , 2.03098 , 0.00000 , 0.98100 | 0.10122
+1.86561 | 1.86561 , 18.93745 , 1.00000 , 19.30162 | 1.76561 , 16.89503 , 1.00000 , 18.32062 | 0.10000 , 2.04242 , 0.00000 , 0.98100 | 0.10121
+1.87659 | 1.87659 , 19.15002 , 1.00000 , 19.40936 | 1.77659 , 17.09623 , 1.00000 , 18.42836 | 0.10000 , 2.05378 , 0.00000 , 0.98100 | 0.10119
+1.88751 | 1.88751 , 19.36250 , 1.00000 , 19.51646 | 1.78751 , 17.29742 , 1.00000 , 18.53546 | 0.10000 , 2.06508 , 0.00000 , 0.98100 | 0.10118
+1.89836 | 1.89836 , 19.57490 , 1.00000 , 19.62294 | 1.79836 , 17.49860 , 1.00000 , 18.64194 | 0.10000 , 2.07630 , 0.00000 , 0.98100 | 0.10117
+1.90915 | 1.90915 , 19.78722 , 1.00000 , 19.72879 | 1.80915 , 17.69976 , 1.00000 , 18.74779 | 0.10000 , 2.08746 , 0.00000 , 0.98100 | 0.10115
+1.91988 | 1.91988 , 19.99946 , 1.00000 , 19.83405 | 1.81988 , 17.90091 , 1.00000 , 18.85305 | 0.10000 , 2.09855 , 0.00000 , 0.98100 | 0.10114
+1.93055 | 1.93055 , 20.21162 , 1.00000 , 19.93871 | 1.83055 , 18.10205 , 1.00000 , 18.95771 | 0.10000 , 2.10958 , 0.00000 , 0.98100 | 0.10113
+1.94116 | 1.94116 , 20.42371 , 1.00000 , 20.04278 | 1.84116 , 18.30317 , 1.00000 , 19.06178 | 0.10000 , 2.12054 , 0.00000 , 0.98100 | 0.10111
+1.95171 | 1.95171 , 20.63571 , 1.00000 , 20.14628 | 1.85171 , 18.50428 , 1.00000 , 19.16528 | 0.10000 , 2.13143 , 0.00000 , 0.98100 | 0.10110
+1.96220 | 1.96220 , 20.84764 , 1.00000 , 20.24922 | 1.86220 , 18.70538 , 1.00000 , 19.26822 | 0.10000 , 2.14226 , 0.00000 , 0.98100 | 0.10109
+1.97264 | 1.97264 , 21.05950 , 1.00000 , 20.35160 | 1.87264 , 18.90646 , 1.00000 , 19.37060 | 0.10000 , 2.15304 , 0.00000 , 0.98100 | 0.10108
+1.98302 | 1.98302 , 21.27129 , 1.00000 , 20.45343 | 1.88302 , 19.10754 , 1.00000 , 19.47243 | 0.10000 , 2.16375 , 0.00000 , 0.98100 | 0.10107
+1.99335 | 1.99335 , 21.48300 , 1.00000 , 20.55472 | 1.89335 , 19.30860 , 1.00000 , 19.57372 | 0.10000 , 2.17440 , 0.00000 , 0.98100 | 0.10105
+2.00362 | 2.00362 , 21.69465 , 1.00000 , 20.65548 | 1.90362 , 19.50965 , 1.00000 , 19.67448 | 0.10000 , 2.18499 , 0.00000 , 0.98100 | NaN
diff --git a/data_2D-Euler-Fixed.txt b/data_2D-Euler-Fixed.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0f92f710cf1f0ece7e06b78ae8716c3f6d43dd6c
--- /dev/null
+++ b/data_2D-Euler-Fixed.txt
@@ -0,0 +1,21 @@
+h | exact | result | error | error_estimated
+0.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 0.00000 , 0.00000 | NaN
+0.20000 | 0.20000 , 0.39620 , 1.00000 , 2.96200 | 0.10000 , 0.10000 , 1.00000 , 1.98100 | 0.10000 , 0.29620 , 0.00000 , 0.98100 | NaN
+0.30000 | 0.30000 , 0.74145 , 1.00000 , 3.94300 | 0.20000 , 0.29810 , 1.00000 , 2.96200 | 0.10000 , 0.44335 , 0.00000 , 0.98100 | NaN
+0.40000 | 0.40000 , 1.18480 , 1.00000 , 4.92400 | 0.30000 , 0.59430 , 1.00000 , 3.94300 | 0.10000 , 0.59050 , 0.00000 , 0.98100 | NaN
+0.50000 | 0.50000 , 1.72625 , 1.00000 , 5.90500 | 0.40000 , 0.98860 , 1.00000 , 4.92400 | 0.10000 , 0.73765 , 0.00000 , 0.98100 | NaN
+0.60000 | 0.60000 , 2.36580 , 1.00000 , 6.88600 | 0.50000 , 1.48100 , 1.00000 , 5.90500 | 0.10000 , 0.88480 , 0.00000 , 0.98100 | NaN
+0.70000 | 0.70000 , 3.10345 , 1.00000 , 7.86700 | 0.60000 , 2.07150 , 1.00000 , 6.88600 | 0.10000 , 1.03195 , 0.00000 , 0.98100 | NaN
+0.80000 | 0.80000 , 3.93920 , 1.00000 , 8.84800 | 0.70000 , 2.76010 , 1.00000 , 7.86700 | 0.10000 , 1.17910 , 0.00000 , 0.98100 | NaN
+0.90000 | 0.90000 , 4.87305 , 1.00000 , 9.82900 | 0.80000 , 3.54680 , 1.00000 , 8.84800 | 0.10000 , 1.32625 , 0.00000 , 0.98100 | NaN
+1.00000 | 1.00000 , 5.90500 , 1.00000 , 10.81000 | 0.90000 , 4.43160 , 1.00000 , 9.82900 | 0.10000 , 1.47340 , 0.00000 , 0.98100 | NaN
+1.10000 | 1.10000 , 7.03505 , 1.00000 , 11.79100 | 1.00000 , 5.41450 , 1.00000 , 10.81000 | 0.10000 , 1.62055 , 0.00000 , 0.98100 | NaN
+1.20000 | 1.20000 , 8.26320 , 1.00000 , 12.77200 | 1.10000 , 6.49550 , 1.00000 , 11.79100 | 0.10000 , 1.76770 , 0.00000 , 0.98100 | NaN
+1.30000 | 1.30000 , 9.58945 , 1.00000 , 13.75300 | 1.20000 , 7.67460 , 1.00000 , 12.77200 | 0.10000 , 1.91485 , 0.00000 , 0.98100 | NaN
+1.40000 | 1.40000 , 11.01380 , 1.00000 , 14.73400 | 1.30000 , 8.95180 , 1.00000 , 13.75300 | 0.10000 , 2.06200 , 0.00000 , 0.98100 | NaN
+1.50000 | 1.50000 , 12.53625 , 1.00000 , 15.71500 | 1.40000 , 10.32710 , 1.00000 , 14.73400 | 0.10000 , 2.20915 , 0.00000 , 0.98100 | NaN
+1.60000 | 1.60000 , 14.15680 , 1.00000 , 16.69600 | 1.50000 , 11.80050 , 1.00000 , 15.71500 | 0.10000 , 2.35630 , 0.00000 , 0.98100 | NaN
+1.70000 | 1.70000 , 15.87545 , 1.00000 , 17.67700 | 1.60000 , 13.37200 , 1.00000 , 16.69600 | 0.10000 , 2.50345 , 0.00000 , 0.98100 | NaN
+1.80000 | 1.80000 , 17.69220 , 1.00000 , 18.65800 | 1.70000 , 15.04160 , 1.00000 , 17.67700 | 0.10000 , 2.65060 , 0.00000 , 0.98100 | NaN
+1.90000 | 1.90000 , 19.60705 , 1.00000 , 19.63900 | 1.80000 , 16.80930 , 1.00000 , 18.65800 | 0.10000 , 2.79775 , 0.00000 , 0.98100 | NaN
+2.00000 | 2.00000 , 21.62000 , 1.00000 , 20.62000 | 1.90000 , 18.67510 , 1.00000 , 19.63900 | 0.10000 , 2.94490 , 0.00000 , 0.98100 | NaN
diff --git a/data_2D-Midpoint-Adaptive.txt b/data_2D-Midpoint-Adaptive.txt
new file mode 100644
index 0000000000000000000000000000000000000000..238f8b0adfc63174aca267ae7fd3983f32679728
--- /dev/null
+++ b/data_2D-Midpoint-Adaptive.txt
@@ -0,0 +1,118 @@
+h | exact | result | error | error_estimated
+0.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 0.00000 , 0.00000 | 0.49050
+0.14515 | 0.14515 , 0.24850 , 1.00000 , 2.42394 | 0.04515 , 0.05515 , 1.00000 , 1.44294 | 0.10000 , 0.19334 , 0.00000 , 0.98100 | 0.22147
+0.17549 | 0.17549 , 0.32656 , 1.00000 , 2.72158 | 0.07549 , 0.10345 , 1.00000 , 1.74058 | 0.10000 , 0.22311 , 0.00000 , 0.98100 | 0.14882
+0.20036 | 0.20036 , 0.39728 , 1.00000 , 2.96557 | 0.10036 , 0.14977 , 1.00000 , 1.98457 | 0.10000 , 0.24751 , 0.00000 , 0.98100 | 0.12199
+0.22288 | 0.22288 , 0.46654 , 1.00000 , 3.18647 | 0.12288 , 0.19695 , 1.00000 , 2.20547 | 0.10000 , 0.26960 , 0.00000 , 0.98100 | 0.11045
+0.24431 | 0.24431 , 0.53707 , 1.00000 , 3.39666 | 0.14431 , 0.24645 , 1.00000 , 2.41566 | 0.10000 , 0.29062 , 0.00000 , 0.98100 | 0.10510
+0.26521 | 0.26521 , 0.61020 , 1.00000 , 3.60169 | 0.16521 , 0.29908 , 1.00000 , 2.62069 | 0.10000 , 0.31112 , 0.00000 , 0.98100 | 0.10252
+0.28585 | 0.28585 , 0.68664 , 1.00000 , 3.80419 | 0.18585 , 0.35527 , 1.00000 , 2.82319 | 0.10000 , 0.33137 , 0.00000 , 0.98100 | 0.10125
+0.30636 | 0.30636 , 0.76674 , 1.00000 , 4.00543 | 0.20636 , 0.41525 , 1.00000 , 3.02443 | 0.10000 , 0.35149 , 0.00000 , 0.98100 | 0.10062
+0.32682 | 0.32682 , 0.85071 , 1.00000 , 4.20606 | 0.22682 , 0.47915 , 1.00000 , 3.22506 | 0.10000 , 0.37156 , 0.00000 , 0.98100 | 0.10031
+0.34723 | 0.34723 , 0.93864 , 1.00000 , 4.40637 | 0.24723 , 0.54705 , 1.00000 , 3.42537 | 0.10000 , 0.39159 , 0.00000 , 0.98100 | 0.10016
+0.36764 | 0.36764 , 1.03058 , 1.00000 , 4.60652 | 0.26764 , 0.61898 , 1.00000 , 3.62552 | 0.10000 , 0.41160 , 0.00000 , 0.98100 | 0.10008
+0.38803 | 0.38803 , 1.12658 , 1.00000 , 4.80660 | 0.28803 , 0.69497 , 1.00000 , 3.82560 | 0.10000 , 0.43161 , 0.00000 , 0.98100 | 0.10004
+0.40842 | 0.40842 , 1.22663 , 1.00000 , 5.00664 | 0.30842 , 0.77501 , 1.00000 , 4.02564 | 0.10000 , 0.45161 , 0.00000 , 0.98100 | 0.10002
+0.42881 | 0.42881 , 1.33075 , 1.00000 , 5.20666 | 0.32881 , 0.85913 , 1.00000 , 4.22566 | 0.10000 , 0.47162 , 0.00000 , 0.98100 | 0.10001
+0.44920 | 0.44920 , 1.43894 , 1.00000 , 5.40667 | 0.34920 , 0.94733 , 1.00000 , 4.42567 | 0.10000 , 0.49162 , 0.00000 , 0.98100 | 0.10000
+0.46959 | 0.46959 , 1.55121 , 1.00000 , 5.60667 | 0.36959 , 1.03960 , 1.00000 , 4.62567 | 0.10000 , 0.51162 , 0.00000 , 0.98100 | 0.10000
+0.48998 | 0.48998 , 1.66756 , 1.00000 , 5.80668 | 0.38998 , 1.13594 , 1.00000 , 4.82568 | 0.10000 , 0.53162 , 0.00000 , 0.98100 | 0.10000
+0.51036 | 0.51036 , 1.78798 , 1.00000 , 6.00668 | 0.41036 , 1.23636 , 1.00000 , 5.02568 | 0.10000 , 0.55162 , 0.00000 , 0.98100 | 0.10000
+0.53075 | 0.53075 , 1.91248 , 1.00000 , 6.20668 | 0.43075 , 1.34086 , 1.00000 , 5.22568 | 0.10000 , 0.57162 , 0.00000 , 0.98100 | 0.10000
+0.55114 | 0.55114 , 2.04106 , 1.00000 , 6.40668 | 0.45114 , 1.44944 , 1.00000 , 5.42568 | 0.10000 , 0.59162 , 0.00000 , 0.98100 | 0.10000
+0.57153 | 0.57153 , 2.17371 , 1.00000 , 6.60668 | 0.47153 , 1.56209 , 1.00000 , 5.62568 | 0.10000 , 0.61162 , 0.00000 , 0.98100 | 0.10000
+0.59191 | 0.59191 , 2.31044 , 1.00000 , 6.80668 | 0.49191 , 1.67882 , 1.00000 , 5.82568 | 0.10000 , 0.63162 , 0.00000 , 0.98100 | 0.10000
+0.61230 | 0.61230 , 2.45125 , 1.00000 , 7.00668 | 0.51230 , 1.79963 , 1.00000 , 6.02568 | 0.10000 , 0.65162 , 0.00000 , 0.98100 | 0.10000
+0.63269 | 0.63269 , 2.59614 , 1.00000 , 7.20668 | 0.53269 , 1.92452 , 1.00000 , 6.22568 | 0.10000 , 0.67162 , 0.00000 , 0.98100 | 0.10000
+0.65308 | 0.65308 , 2.74510 , 1.00000 , 7.40668 | 0.55308 , 2.05348 , 1.00000 , 6.42568 | 0.10000 , 0.69162 , 0.00000 , 0.98100 | 0.10000
+0.67346 | 0.67346 , 2.89814 , 1.00000 , 7.60668 | 0.57346 , 2.18652 , 1.00000 , 6.62568 | 0.10000 , 0.71162 , 0.00000 , 0.98100 | 0.10000
+0.69385 | 0.69385 , 3.05526 , 1.00000 , 7.80668 | 0.59385 , 2.32364 , 1.00000 , 6.82568 | 0.10000 , 0.73162 , 0.00000 , 0.98100 | 0.10000
+0.71424 | 0.71424 , 3.21646 , 1.00000 , 8.00668 | 0.61424 , 2.46484 , 1.00000 , 7.02568 | 0.10000 , 0.75162 , 0.00000 , 0.98100 | 0.10000
+0.73463 | 0.73463 , 3.38173 , 1.00000 , 8.20668 | 0.63463 , 2.61011 , 1.00000 , 7.22568 | 0.10000 , 0.77162 , 0.00000 , 0.98100 | 0.10000
+0.75501 | 0.75501 , 3.55108 , 1.00000 , 8.40668 | 0.65501 , 2.75946 , 1.00000 , 7.42568 | 0.10000 , 0.79162 , 0.00000 , 0.98100 | 0.10000
+0.77540 | 0.77540 , 3.72451 , 1.00000 , 8.60668 | 0.67540 , 2.91289 , 1.00000 , 7.62568 | 0.10000 , 0.81162 , 0.00000 , 0.98100 | 0.10000
+0.79579 | 0.79579 , 3.90202 , 1.00000 , 8.80668 | 0.69579 , 3.07040 , 1.00000 , 7.82568 | 0.10000 , 0.83162 , 0.00000 , 0.98100 | 0.10000
+0.81618 | 0.81618 , 4.08360 , 1.00000 , 9.00668 | 0.71618 , 3.23198 , 1.00000 , 8.02568 | 0.10000 , 0.85162 , 0.00000 , 0.98100 | 0.10000
+0.83656 | 0.83656 , 4.26926 , 1.00000 , 9.20668 | 0.73656 , 3.39764 , 1.00000 , 8.22568 | 0.10000 , 0.87162 , 0.00000 , 0.98100 | 0.10000
+0.85695 | 0.85695 , 4.45900 , 1.00000 , 9.40668 | 0.75695 , 3.56738 , 1.00000 , 8.42568 | 0.10000 , 0.89162 , 0.00000 , 0.98100 | 0.10000
+0.87734 | 0.87734 , 4.65282 , 1.00000 , 9.60668 | 0.77734 , 3.74120 , 1.00000 , 8.62568 | 0.10000 , 0.91162 , 0.00000 , 0.98100 | 0.10000
+0.89772 | 0.89772 , 4.85071 , 1.00000 , 9.80668 | 0.79772 , 3.91909 , 1.00000 , 8.82568 | 0.10000 , 0.93162 , 0.00000 , 0.98100 | 0.10000
+0.91811 | 0.91811 , 5.05268 , 1.00000 , 10.00668 | 0.81811 , 4.10106 , 1.00000 , 9.02568 | 0.10000 , 0.95162 , 0.00000 , 0.98100 | 0.10000
+0.93850 | 0.93850 , 5.25873 , 1.00000 , 10.20668 | 0.83850 , 4.28711 , 1.00000 , 9.22568 | 0.10000 , 0.97162 , 0.00000 , 0.98100 | 0.10000
+0.95889 | 0.95889 , 5.46886 , 1.00000 , 10.40668 | 0.85889 , 4.47724 , 1.00000 , 9.42568 | 0.10000 , 0.99162 , 0.00000 , 0.98100 | 0.10000
+0.97927 | 0.97927 , 5.68306 , 1.00000 , 10.60668 | 0.87927 , 4.67144 , 1.00000 , 9.62568 | 0.10000 , 1.01162 , 0.00000 , 0.98100 | 0.10000
+0.99966 | 0.99966 , 5.90134 , 1.00000 , 10.80668 | 0.89966 , 4.86972 , 1.00000 , 9.82568 | 0.10000 , 1.03162 , 0.00000 , 0.98100 | 0.10169
+1.01988 | 1.01988 , 6.12183 , 1.00000 , 11.00501 | 0.91988 , 5.07038 , 1.00000 , 10.02401 | 0.10000 , 1.05145 , 0.00000 , 0.98100 | 0.10283
+1.03982 | 1.03982 , 6.34318 , 1.00000 , 11.20059 | 0.93982 , 5.27217 , 1.00000 , 10.21959 | 0.10000 , 1.07101 , 0.00000 , 0.98100 | 0.10334
+1.05943 | 1.05943 , 6.56474 , 1.00000 , 11.39299 | 0.95943 , 5.47449 , 1.00000 , 10.41199 | 0.10000 , 1.09025 , 0.00000 , 0.98100 | 0.10352
+1.07870 | 1.07870 , 6.78618 , 1.00000 , 11.58209 | 0.97870 , 5.67702 , 1.00000 , 10.60109 | 0.10000 , 1.10916 , 0.00000 , 0.98100 | 0.10354
+1.09765 | 1.09765 , 7.00735 , 1.00000 , 11.76793 | 0.99765 , 5.87961 , 1.00000 , 10.78693 | 0.10000 , 1.12774 , 0.00000 , 0.98100 | 0.10349
+1.11627 | 1.11627 , 7.22818 , 1.00000 , 11.95061 | 1.01627 , 6.08217 , 1.00000 , 10.96961 | 0.10000 , 1.14601 , 0.00000 , 0.98100 | 0.10341
+1.13458 | 1.13458 , 7.44867 , 1.00000 , 12.13024 | 1.03458 , 6.28469 , 1.00000 , 11.14924 | 0.10000 , 1.16397 , 0.00000 , 0.98100 | 0.10331
+1.15260 | 1.15260 , 7.66879 , 1.00000 , 12.30698 | 1.05260 , 6.48714 , 1.00000 , 11.32598 | 0.10000 , 1.18165 , 0.00000 , 0.98100 | 0.10322
+1.17033 | 1.17033 , 7.88857 , 1.00000 , 12.48094 | 1.07033 , 6.68953 , 1.00000 , 11.49994 | 0.10000 , 1.19904 , 0.00000 , 0.98100 | 0.10312
+1.18779 | 1.18779 , 8.10801 , 1.00000 , 12.65224 | 1.08779 , 6.89184 , 1.00000 , 11.67124 | 0.10000 , 1.21617 , 0.00000 , 0.98100 | 0.10303
+1.20500 | 1.20500 , 8.32714 , 1.00000 , 12.82101 | 1.10500 , 7.09408 , 1.00000 , 11.84001 | 0.10000 , 1.23305 , 0.00000 , 0.98100 | 0.10294
+1.22195 | 1.22195 , 8.54595 , 1.00000 , 12.98736 | 1.12195 , 7.29626 , 1.00000 , 12.00636 | 0.10000 , 1.24969 , 0.00000 , 0.98100 | 0.10285
+1.23867 | 1.23867 , 8.76447 , 1.00000 , 13.15138 | 1.13867 , 7.49838 , 1.00000 , 12.17038 | 0.10000 , 1.26609 , 0.00000 , 0.98100 | 0.10277
+1.25517 | 1.25517 , 8.98271 , 1.00000 , 13.31318 | 1.15517 , 7.70044 , 1.00000 , 12.33218 | 0.10000 , 1.28227 , 0.00000 , 0.98100 | 0.10270
+1.27144 | 1.27144 , 9.20068 , 1.00000 , 13.47284 | 1.17144 , 7.90245 , 1.00000 , 12.49184 | 0.10000 , 1.29823 , 0.00000 , 0.98100 | 0.10263
+1.28751 | 1.28751 , 9.41839 , 1.00000 , 13.63044 | 1.18751 , 8.10440 , 1.00000 , 12.64944 | 0.10000 , 1.31399 , 0.00000 , 0.98100 | 0.10256
+1.30337 | 1.30337 , 9.63585 , 1.00000 , 13.78606 | 1.20337 , 8.30630 , 1.00000 , 12.80506 | 0.10000 , 1.32956 , 0.00000 , 0.98100 | 0.10249
+1.31904 | 1.31904 , 9.85308 , 1.00000 , 13.93978 | 1.21904 , 8.50815 , 1.00000 , 12.95878 | 0.10000 , 1.34493 , 0.00000 , 0.98100 | 0.10243
+1.33452 | 1.33452 , 10.07008 , 1.00000 , 14.09166 | 1.23452 , 8.70996 , 1.00000 , 13.11066 | 0.10000 , 1.36012 , 0.00000 , 0.98100 | 0.10237
+1.34982 | 1.34982 , 10.28685 , 1.00000 , 14.24177 | 1.24982 , 8.91173 , 1.00000 , 13.26077 | 0.10000 , 1.37513 , 0.00000 , 0.98100 | 0.10232
+1.36495 | 1.36495 , 10.50342 , 1.00000 , 14.39017 | 1.26495 , 9.11345 , 1.00000 , 13.40917 | 0.10000 , 1.38997 , 0.00000 , 0.98100 | 0.10227
+1.37991 | 1.37991 , 10.71978 , 1.00000 , 14.53692 | 1.27991 , 9.31513 , 1.00000 , 13.55592 | 0.10000 , 1.40464 , 0.00000 , 0.98100 | 0.10221
+1.39471 | 1.39471 , 10.93594 , 1.00000 , 14.68207 | 1.29471 , 9.51678 , 1.00000 , 13.70107 | 0.10000 , 1.41916 , 0.00000 , 0.98100 | 0.10217
+1.40934 | 1.40934 , 11.15191 , 1.00000 , 14.82567 | 1.30934 , 9.71839 , 1.00000 , 13.84467 | 0.10000 , 1.43352 , 0.00000 , 0.98100 | 0.10212
+1.42383 | 1.42383 , 11.36770 , 1.00000 , 14.96777 | 1.32383 , 9.91997 , 1.00000 , 13.98677 | 0.10000 , 1.44773 , 0.00000 , 0.98100 | 0.10208
+1.43817 | 1.43817 , 11.58331 , 1.00000 , 15.10843 | 1.33817 , 10.12152 , 1.00000 , 14.12743 | 0.10000 , 1.46179 , 0.00000 , 0.98100 | 0.10203
+1.45236 | 1.45236 , 11.79875 , 1.00000 , 15.24767 | 1.35236 , 10.32303 , 1.00000 , 14.26667 | 0.10000 , 1.47572 , 0.00000 , 0.98100 | 0.10199
+1.46642 | 1.46642 , 12.01402 , 1.00000 , 15.38555 | 1.36642 , 10.52451 , 1.00000 , 14.40455 | 0.10000 , 1.48950 , 0.00000 , 0.98100 | 0.10195
+1.48034 | 1.48034 , 12.22913 , 1.00000 , 15.52210 | 1.38034 , 10.72597 , 1.00000 , 14.54110 | 0.10000 , 1.50316 , 0.00000 , 0.98100 | 0.10192
+1.49412 | 1.49412 , 12.44408 , 1.00000 , 15.65736 | 1.39412 , 10.92740 , 1.00000 , 14.67636 | 0.10000 , 1.51669 , 0.00000 , 0.98100 | 0.10188
+1.50778 | 1.50778 , 12.65888 , 1.00000 , 15.79137 | 1.40778 , 11.12879 , 1.00000 , 14.81037 | 0.10000 , 1.53009 , 0.00000 , 0.98100 | 0.10184
+1.52132 | 1.52132 , 12.87353 , 1.00000 , 15.92416 | 1.42132 , 11.33017 , 1.00000 , 14.94316 | 0.10000 , 1.54337 , 0.00000 , 0.98100 | 0.10181
+1.53474 | 1.53474 , 13.08804 , 1.00000 , 16.05576 | 1.43474 , 11.53152 , 1.00000 , 15.07476 | 0.10000 , 1.55653 , 0.00000 , 0.98100 | 0.10178
+1.54803 | 1.54803 , 13.30241 , 1.00000 , 16.18621 | 1.44803 , 11.73284 , 1.00000 , 15.20521 | 0.10000 , 1.56957 , 0.00000 , 0.98100 | 0.10175
+1.56122 | 1.56122 , 13.51665 , 1.00000 , 16.31553 | 1.46122 , 11.93414 , 1.00000 , 15.33453 | 0.10000 , 1.58250 , 0.00000 , 0.98100 | 0.10172
+1.57429 | 1.57429 , 13.73075 , 1.00000 , 16.44376 | 1.47429 , 12.13542 , 1.00000 , 15.46276 | 0.10000 , 1.59533 , 0.00000 , 0.98100 | 0.10169
+1.58725 | 1.58725 , 13.94472 , 1.00000 , 16.57092 | 1.48725 , 12.33668 , 1.00000 , 15.58992 | 0.10000 , 1.60804 , 0.00000 , 0.98100 | 0.10166
+1.60011 | 1.60011 , 14.15857 , 1.00000 , 16.69704 | 1.50011 , 12.53792 , 1.00000 , 15.71604 | 0.10000 , 1.62065 , 0.00000 , 0.98100 | 0.10163
+1.61286 | 1.61286 , 14.37230 , 1.00000 , 16.82214 | 1.51286 , 12.73913 , 1.00000 , 15.84114 | 0.10000 , 1.63316 , 0.00000 , 0.98100 | 0.10161
+1.62551 | 1.62551 , 14.58591 , 1.00000 , 16.94625 | 1.52551 , 12.94033 , 1.00000 , 15.96525 | 0.10000 , 1.64558 , 0.00000 , 0.98100 | 0.10158
+1.63806 | 1.63806 , 14.79940 , 1.00000 , 17.06939 | 1.53806 , 13.14151 , 1.00000 , 16.08839 | 0.10000 , 1.65789 , 0.00000 , 0.98100 | 0.10156
+1.65052 | 1.65052 , 15.01278 , 1.00000 , 17.19159 | 1.55052 , 13.34267 , 1.00000 , 16.21059 | 0.10000 , 1.67011 , 0.00000 , 0.98100 | 0.10153
+1.66288 | 1.66288 , 15.22605 , 1.00000 , 17.31286 | 1.56288 , 13.54381 , 1.00000 , 16.33186 | 0.10000 , 1.68224 , 0.00000 , 0.98100 | 0.10151
+1.67515 | 1.67515 , 15.43921 , 1.00000 , 17.43322 | 1.57515 , 13.74494 , 1.00000 , 16.45222 | 0.10000 , 1.69427 , 0.00000 , 0.98100 | 0.10149
+1.68733 | 1.68733 , 15.65226 , 1.00000 , 17.55270 | 1.58733 , 13.94604 , 1.00000 , 16.57170 | 0.10000 , 1.70622 , 0.00000 , 0.98100 | 0.10146
+1.69942 | 1.69942 , 15.86522 , 1.00000 , 17.67132 | 1.59942 , 14.14714 , 1.00000 , 16.69032 | 0.10000 , 1.71808 , 0.00000 , 0.98100 | 0.10144
+1.71143 | 1.71143 , 16.07807 , 1.00000 , 17.78909 | 1.61143 , 14.34821 , 1.00000 , 16.80809 | 0.10000 , 1.72986 , 0.00000 , 0.98100 | 0.10142
+1.72335 | 1.72335 , 16.29083 , 1.00000 , 17.90603 | 1.62335 , 14.54927 , 1.00000 , 16.92503 | 0.10000 , 1.74155 , 0.00000 , 0.98100 | 0.10140
+1.73518 | 1.73518 , 16.50349 , 1.00000 , 18.02216 | 1.63518 , 14.75032 , 1.00000 , 17.04116 | 0.10000 , 1.75317 , 0.00000 , 0.98100 | 0.10138
+1.74694 | 1.74694 , 16.71605 , 1.00000 , 18.13750 | 1.64694 , 14.95135 , 1.00000 , 17.15650 | 0.10000 , 1.76470 , 0.00000 , 0.98100 | 0.10136
+1.75862 | 1.75862 , 16.92852 , 1.00000 , 18.25206 | 1.65862 , 15.15237 , 1.00000 , 17.27106 | 0.10000 , 1.77616 , 0.00000 , 0.98100 | 0.10134
+1.77022 | 1.77022 , 17.14091 , 1.00000 , 18.36585 | 1.67022 , 15.35337 , 1.00000 , 17.38485 | 0.10000 , 1.78754 , 0.00000 , 0.98100 | 0.10133
+1.78174 | 1.78174 , 17.35320 , 1.00000 , 18.47890 | 1.68174 , 15.55436 , 1.00000 , 17.49790 | 0.10000 , 1.79884 , 0.00000 , 0.98100 | 0.10131
+1.79319 | 1.79319 , 17.56541 , 1.00000 , 18.59122 | 1.69319 , 15.75534 , 1.00000 , 17.61022 | 0.10000 , 1.81007 , 0.00000 , 0.98100 | 0.10129
+1.80457 | 1.80457 , 17.77754 , 1.00000 , 18.70281 | 1.70457 , 15.95630 , 1.00000 , 17.72181 | 0.10000 , 1.82123 , 0.00000 , 0.98100 | 0.10128
+1.81587 | 1.81587 , 17.98958 , 1.00000 , 18.81370 | 1.71587 , 16.15726 , 1.00000 , 17.83270 | 0.10000 , 1.83232 , 0.00000 , 0.98100 | 0.10126
+1.82711 | 1.82711 , 18.20154 , 1.00000 , 18.92390 | 1.72711 , 16.35820 , 1.00000 , 17.94290 | 0.10000 , 1.84334 , 0.00000 , 0.98100 | 0.10124
+1.83827 | 1.83827 , 18.41342 , 1.00000 , 19.03342 | 1.73827 , 16.55913 , 1.00000 , 18.05242 | 0.10000 , 1.85429 , 0.00000 , 0.98100 | 0.10123
+1.84937 | 1.84937 , 18.62522 , 1.00000 , 19.14228 | 1.74937 , 16.76004 , 1.00000 , 18.16128 | 0.10000 , 1.86518 , 0.00000 , 0.98100 | 0.10121
+1.86040 | 1.86040 , 18.83695 , 1.00000 , 19.25048 | 1.76040 , 16.96095 , 1.00000 , 18.26948 | 0.10000 , 1.87600 , 0.00000 , 0.98100 | 0.10120
+1.87136 | 1.87136 , 19.04860 , 1.00000 , 19.35803 | 1.77136 , 17.16184 , 1.00000 , 18.37703 | 0.10000 , 1.88675 , 0.00000 , 0.98100 | 0.10118
+1.88226 | 1.88226 , 19.26017 , 1.00000 , 19.46496 | 1.78226 , 17.36273 , 1.00000 , 18.48396 | 0.10000 , 1.89745 , 0.00000 , 0.98100 | 0.10117
+1.89310 | 1.89310 , 19.47168 , 1.00000 , 19.57126 | 1.79310 , 17.56360 , 1.00000 , 18.59026 | 0.10000 , 1.90808 , 0.00000 , 0.98100 | 0.10116
+1.90387 | 1.90387 , 19.68311 , 1.00000 , 19.67696 | 1.80387 , 17.76447 , 1.00000 , 18.69596 | 0.10000 , 1.91865 , 0.00000 , 0.98100 | 0.10114
+1.91458 | 1.91458 , 19.89448 , 1.00000 , 19.78205 | 1.81458 , 17.96532 , 1.00000 , 18.80105 | 0.10000 , 1.92916 , 0.00000 , 0.98100 | 0.10113
+1.92524 | 1.92524 , 20.10577 , 1.00000 , 19.88656 | 1.82524 , 18.16617 , 1.00000 , 18.90556 | 0.10000 , 1.93961 , 0.00000 , 0.98100 | 0.10112
+1.93583 | 1.93583 , 20.31700 , 1.00000 , 19.99049 | 1.83583 , 18.36700 , 1.00000 , 19.00949 | 0.10000 , 1.95000 , 0.00000 , 0.98100 | 0.10111
+1.94637 | 1.94637 , 20.52816 , 1.00000 , 20.09384 | 1.84637 , 18.56783 , 1.00000 , 19.11284 | 0.10000 , 1.96033 , 0.00000 , 0.98100 | 0.10109
+1.95684 | 1.95684 , 20.73926 , 1.00000 , 20.19664 | 1.85684 , 18.76864 , 1.00000 , 19.21564 | 0.10000 , 1.97061 , 0.00000 , 0.98100 | 0.10108
+1.96727 | 1.96727 , 20.95029 , 1.00000 , 20.29888 | 1.86727 , 18.96945 , 1.00000 , 19.31788 | 0.10000 , 1.98084 , 0.00000 , 0.98100 | 0.10107
+1.97763 | 1.97763 , 21.16126 , 1.00000 , 20.40059 | 1.87763 , 19.17025 , 1.00000 , 19.41959 | 0.10000 , 1.99101 , 0.00000 , 0.98100 | 0.10106
+1.98795 | 1.98795 , 21.37217 , 1.00000 , 20.50175 | 1.88795 , 19.37104 , 1.00000 , 19.52075 | 0.10000 , 2.00113 , 0.00000 , 0.98100 | 0.10105
+1.99821 | 1.99821 , 21.58301 , 1.00000 , 20.60240 | 1.89821 , 19.57182 , 1.00000 , 19.62140 | 0.10000 , 2.01119 , 0.00000 , 0.98100 | 0.10104
+2.00841 | 2.00841 , 21.79380 , 1.00000 , 20.70252 | 1.90841 , 19.77260 , 1.00000 , 19.72152 | 0.10000 , 2.02120 , 0.00000 , 0.98100 | NaN
diff --git a/data_2D-Midpoint-Fixed.txt b/data_2D-Midpoint-Fixed.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9e0d5526ec51440dea41324655dfd72d9e0bcbcb
--- /dev/null
+++ b/data_2D-Midpoint-Fixed.txt
@@ -0,0 +1,21 @@
+h | exact | result | error | error_estimated
+0.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 0.00000 , 0.00000 | NaN
+0.20000 | 0.20000 , 0.39620 , 1.00000 , 2.96200 | 0.10000 , 0.14905 , 1.00000 , 1.98100 | 0.10000 , 0.24715 , 0.00000 , 0.98100 | NaN
+0.30000 | 0.30000 , 0.74145 , 1.00000 , 3.94300 | 0.20000 , 0.39620 , 1.00000 , 2.96200 | 0.10000 , 0.34525 , 0.00000 , 0.98100 | NaN
+0.40000 | 0.40000 , 1.18480 , 1.00000 , 4.92400 | 0.30000 , 0.74145 , 1.00000 , 3.94300 | 0.10000 , 0.44335 , 0.00000 , 0.98100 | NaN
+0.50000 | 0.50000 , 1.72625 , 1.00000 , 5.90500 | 0.40000 , 1.18480 , 1.00000 , 4.92400 | 0.10000 , 0.54145 , 0.00000 , 0.98100 | NaN
+0.60000 | 0.60000 , 2.36580 , 1.00000 , 6.88600 | 0.50000 , 1.72625 , 1.00000 , 5.90500 | 0.10000 , 0.63955 , 0.00000 , 0.98100 | NaN
+0.70000 | 0.70000 , 3.10345 , 1.00000 , 7.86700 | 0.60000 , 2.36580 , 1.00000 , 6.88600 | 0.10000 , 0.73765 , 0.00000 , 0.98100 | NaN
+0.80000 | 0.80000 , 3.93920 , 1.00000 , 8.84800 | 0.70000 , 3.10345 , 1.00000 , 7.86700 | 0.10000 , 0.83575 , 0.00000 , 0.98100 | NaN
+0.90000 | 0.90000 , 4.87305 , 1.00000 , 9.82900 | 0.80000 , 3.93920 , 1.00000 , 8.84800 | 0.10000 , 0.93385 , 0.00000 , 0.98100 | NaN
+1.00000 | 1.00000 , 5.90500 , 1.00000 , 10.81000 | 0.90000 , 4.87305 , 1.00000 , 9.82900 | 0.10000 , 1.03195 , 0.00000 , 0.98100 | NaN
+1.10000 | 1.10000 , 7.03505 , 1.00000 , 11.79100 | 1.00000 , 5.90500 , 1.00000 , 10.81000 | 0.10000 , 1.13005 , 0.00000 , 0.98100 | NaN
+1.20000 | 1.20000 , 8.26320 , 1.00000 , 12.77200 | 1.10000 , 7.03505 , 1.00000 , 11.79100 | 0.10000 , 1.22815 , 0.00000 , 0.98100 | NaN
+1.30000 | 1.30000 , 9.58945 , 1.00000 , 13.75300 | 1.20000 , 8.26320 , 1.00000 , 12.77200 | 0.10000 , 1.32625 , 0.00000 , 0.98100 | NaN
+1.40000 | 1.40000 , 11.01380 , 1.00000 , 14.73400 | 1.30000 , 9.58945 , 1.00000 , 13.75300 | 0.10000 , 1.42435 , 0.00000 , 0.98100 | NaN
+1.50000 | 1.50000 , 12.53625 , 1.00000 , 15.71500 | 1.40000 , 11.01380 , 1.00000 , 14.73400 | 0.10000 , 1.52245 , 0.00000 , 0.98100 | NaN
+1.60000 | 1.60000 , 14.15680 , 1.00000 , 16.69600 | 1.50000 , 12.53625 , 1.00000 , 15.71500 | 0.10000 , 1.62055 , 0.00000 , 0.98100 | NaN
+1.70000 | 1.70000 , 15.87545 , 1.00000 , 17.67700 | 1.60000 , 14.15680 , 1.00000 , 16.69600 | 0.10000 , 1.71865 , 0.00000 , 0.98100 | NaN
+1.80000 | 1.80000 , 17.69220 , 1.00000 , 18.65800 | 1.70000 , 15.87545 , 1.00000 , 17.67700 | 0.10000 , 1.81675 , 0.00000 , 0.98100 | NaN
+1.90000 | 1.90000 , 19.60705 , 1.00000 , 19.63900 | 1.80000 , 17.69220 , 1.00000 , 18.65800 | 0.10000 , 1.91485 , 0.00000 , 0.98100 | NaN
+2.00000 | 2.00000 , 21.62000 , 1.00000 , 20.62000 | 1.90000 , 19.60705 , 1.00000 , 19.63900 | 0.10000 , 2.01295 , 0.00000 , 0.98100 | NaN
diff --git a/data_2D-Runge-Kutta-Adaptive.txt b/data_2D-Runge-Kutta-Adaptive.txt
new file mode 100644
index 0000000000000000000000000000000000000000..238f8b0adfc63174aca267ae7fd3983f32679728
--- /dev/null
+++ b/data_2D-Runge-Kutta-Adaptive.txt
@@ -0,0 +1,118 @@
+h | exact | result | error | error_estimated
+0.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 0.00000 , 0.00000 | 0.49050
+0.14515 | 0.14515 , 0.24850 , 1.00000 , 2.42394 | 0.04515 , 0.05515 , 1.00000 , 1.44294 | 0.10000 , 0.19334 , 0.00000 , 0.98100 | 0.22147
+0.17549 | 0.17549 , 0.32656 , 1.00000 , 2.72158 | 0.07549 , 0.10345 , 1.00000 , 1.74058 | 0.10000 , 0.22311 , 0.00000 , 0.98100 | 0.14882
+0.20036 | 0.20036 , 0.39728 , 1.00000 , 2.96557 | 0.10036 , 0.14977 , 1.00000 , 1.98457 | 0.10000 , 0.24751 , 0.00000 , 0.98100 | 0.12199
+0.22288 | 0.22288 , 0.46654 , 1.00000 , 3.18647 | 0.12288 , 0.19695 , 1.00000 , 2.20547 | 0.10000 , 0.26960 , 0.00000 , 0.98100 | 0.11045
+0.24431 | 0.24431 , 0.53707 , 1.00000 , 3.39666 | 0.14431 , 0.24645 , 1.00000 , 2.41566 | 0.10000 , 0.29062 , 0.00000 , 0.98100 | 0.10510
+0.26521 | 0.26521 , 0.61020 , 1.00000 , 3.60169 | 0.16521 , 0.29908 , 1.00000 , 2.62069 | 0.10000 , 0.31112 , 0.00000 , 0.98100 | 0.10252
+0.28585 | 0.28585 , 0.68664 , 1.00000 , 3.80419 | 0.18585 , 0.35527 , 1.00000 , 2.82319 | 0.10000 , 0.33137 , 0.00000 , 0.98100 | 0.10125
+0.30636 | 0.30636 , 0.76674 , 1.00000 , 4.00543 | 0.20636 , 0.41525 , 1.00000 , 3.02443 | 0.10000 , 0.35149 , 0.00000 , 0.98100 | 0.10062
+0.32682 | 0.32682 , 0.85071 , 1.00000 , 4.20606 | 0.22682 , 0.47915 , 1.00000 , 3.22506 | 0.10000 , 0.37156 , 0.00000 , 0.98100 | 0.10031
+0.34723 | 0.34723 , 0.93864 , 1.00000 , 4.40637 | 0.24723 , 0.54705 , 1.00000 , 3.42537 | 0.10000 , 0.39159 , 0.00000 , 0.98100 | 0.10016
+0.36764 | 0.36764 , 1.03058 , 1.00000 , 4.60652 | 0.26764 , 0.61898 , 1.00000 , 3.62552 | 0.10000 , 0.41160 , 0.00000 , 0.98100 | 0.10008
+0.38803 | 0.38803 , 1.12658 , 1.00000 , 4.80660 | 0.28803 , 0.69497 , 1.00000 , 3.82560 | 0.10000 , 0.43161 , 0.00000 , 0.98100 | 0.10004
+0.40842 | 0.40842 , 1.22663 , 1.00000 , 5.00664 | 0.30842 , 0.77501 , 1.00000 , 4.02564 | 0.10000 , 0.45161 , 0.00000 , 0.98100 | 0.10002
+0.42881 | 0.42881 , 1.33075 , 1.00000 , 5.20666 | 0.32881 , 0.85913 , 1.00000 , 4.22566 | 0.10000 , 0.47162 , 0.00000 , 0.98100 | 0.10001
+0.44920 | 0.44920 , 1.43894 , 1.00000 , 5.40667 | 0.34920 , 0.94733 , 1.00000 , 4.42567 | 0.10000 , 0.49162 , 0.00000 , 0.98100 | 0.10000
+0.46959 | 0.46959 , 1.55121 , 1.00000 , 5.60667 | 0.36959 , 1.03960 , 1.00000 , 4.62567 | 0.10000 , 0.51162 , 0.00000 , 0.98100 | 0.10000
+0.48998 | 0.48998 , 1.66756 , 1.00000 , 5.80668 | 0.38998 , 1.13594 , 1.00000 , 4.82568 | 0.10000 , 0.53162 , 0.00000 , 0.98100 | 0.10000
+0.51036 | 0.51036 , 1.78798 , 1.00000 , 6.00668 | 0.41036 , 1.23636 , 1.00000 , 5.02568 | 0.10000 , 0.55162 , 0.00000 , 0.98100 | 0.10000
+0.53075 | 0.53075 , 1.91248 , 1.00000 , 6.20668 | 0.43075 , 1.34086 , 1.00000 , 5.22568 | 0.10000 , 0.57162 , 0.00000 , 0.98100 | 0.10000
+0.55114 | 0.55114 , 2.04106 , 1.00000 , 6.40668 | 0.45114 , 1.44944 , 1.00000 , 5.42568 | 0.10000 , 0.59162 , 0.00000 , 0.98100 | 0.10000
+0.57153 | 0.57153 , 2.17371 , 1.00000 , 6.60668 | 0.47153 , 1.56209 , 1.00000 , 5.62568 | 0.10000 , 0.61162 , 0.00000 , 0.98100 | 0.10000
+0.59191 | 0.59191 , 2.31044 , 1.00000 , 6.80668 | 0.49191 , 1.67882 , 1.00000 , 5.82568 | 0.10000 , 0.63162 , 0.00000 , 0.98100 | 0.10000
+0.61230 | 0.61230 , 2.45125 , 1.00000 , 7.00668 | 0.51230 , 1.79963 , 1.00000 , 6.02568 | 0.10000 , 0.65162 , 0.00000 , 0.98100 | 0.10000
+0.63269 | 0.63269 , 2.59614 , 1.00000 , 7.20668 | 0.53269 , 1.92452 , 1.00000 , 6.22568 | 0.10000 , 0.67162 , 0.00000 , 0.98100 | 0.10000
+0.65308 | 0.65308 , 2.74510 , 1.00000 , 7.40668 | 0.55308 , 2.05348 , 1.00000 , 6.42568 | 0.10000 , 0.69162 , 0.00000 , 0.98100 | 0.10000
+0.67346 | 0.67346 , 2.89814 , 1.00000 , 7.60668 | 0.57346 , 2.18652 , 1.00000 , 6.62568 | 0.10000 , 0.71162 , 0.00000 , 0.98100 | 0.10000
+0.69385 | 0.69385 , 3.05526 , 1.00000 , 7.80668 | 0.59385 , 2.32364 , 1.00000 , 6.82568 | 0.10000 , 0.73162 , 0.00000 , 0.98100 | 0.10000
+0.71424 | 0.71424 , 3.21646 , 1.00000 , 8.00668 | 0.61424 , 2.46484 , 1.00000 , 7.02568 | 0.10000 , 0.75162 , 0.00000 , 0.98100 | 0.10000
+0.73463 | 0.73463 , 3.38173 , 1.00000 , 8.20668 | 0.63463 , 2.61011 , 1.00000 , 7.22568 | 0.10000 , 0.77162 , 0.00000 , 0.98100 | 0.10000
+0.75501 | 0.75501 , 3.55108 , 1.00000 , 8.40668 | 0.65501 , 2.75946 , 1.00000 , 7.42568 | 0.10000 , 0.79162 , 0.00000 , 0.98100 | 0.10000
+0.77540 | 0.77540 , 3.72451 , 1.00000 , 8.60668 | 0.67540 , 2.91289 , 1.00000 , 7.62568 | 0.10000 , 0.81162 , 0.00000 , 0.98100 | 0.10000
+0.79579 | 0.79579 , 3.90202 , 1.00000 , 8.80668 | 0.69579 , 3.07040 , 1.00000 , 7.82568 | 0.10000 , 0.83162 , 0.00000 , 0.98100 | 0.10000
+0.81618 | 0.81618 , 4.08360 , 1.00000 , 9.00668 | 0.71618 , 3.23198 , 1.00000 , 8.02568 | 0.10000 , 0.85162 , 0.00000 , 0.98100 | 0.10000
+0.83656 | 0.83656 , 4.26926 , 1.00000 , 9.20668 | 0.73656 , 3.39764 , 1.00000 , 8.22568 | 0.10000 , 0.87162 , 0.00000 , 0.98100 | 0.10000
+0.85695 | 0.85695 , 4.45900 , 1.00000 , 9.40668 | 0.75695 , 3.56738 , 1.00000 , 8.42568 | 0.10000 , 0.89162 , 0.00000 , 0.98100 | 0.10000
+0.87734 | 0.87734 , 4.65282 , 1.00000 , 9.60668 | 0.77734 , 3.74120 , 1.00000 , 8.62568 | 0.10000 , 0.91162 , 0.00000 , 0.98100 | 0.10000
+0.89772 | 0.89772 , 4.85071 , 1.00000 , 9.80668 | 0.79772 , 3.91909 , 1.00000 , 8.82568 | 0.10000 , 0.93162 , 0.00000 , 0.98100 | 0.10000
+0.91811 | 0.91811 , 5.05268 , 1.00000 , 10.00668 | 0.81811 , 4.10106 , 1.00000 , 9.02568 | 0.10000 , 0.95162 , 0.00000 , 0.98100 | 0.10000
+0.93850 | 0.93850 , 5.25873 , 1.00000 , 10.20668 | 0.83850 , 4.28711 , 1.00000 , 9.22568 | 0.10000 , 0.97162 , 0.00000 , 0.98100 | 0.10000
+0.95889 | 0.95889 , 5.46886 , 1.00000 , 10.40668 | 0.85889 , 4.47724 , 1.00000 , 9.42568 | 0.10000 , 0.99162 , 0.00000 , 0.98100 | 0.10000
+0.97927 | 0.97927 , 5.68306 , 1.00000 , 10.60668 | 0.87927 , 4.67144 , 1.00000 , 9.62568 | 0.10000 , 1.01162 , 0.00000 , 0.98100 | 0.10000
+0.99966 | 0.99966 , 5.90134 , 1.00000 , 10.80668 | 0.89966 , 4.86972 , 1.00000 , 9.82568 | 0.10000 , 1.03162 , 0.00000 , 0.98100 | 0.10169
+1.01988 | 1.01988 , 6.12183 , 1.00000 , 11.00501 | 0.91988 , 5.07038 , 1.00000 , 10.02401 | 0.10000 , 1.05145 , 0.00000 , 0.98100 | 0.10283
+1.03982 | 1.03982 , 6.34318 , 1.00000 , 11.20059 | 0.93982 , 5.27217 , 1.00000 , 10.21959 | 0.10000 , 1.07101 , 0.00000 , 0.98100 | 0.10334
+1.05943 | 1.05943 , 6.56474 , 1.00000 , 11.39299 | 0.95943 , 5.47449 , 1.00000 , 10.41199 | 0.10000 , 1.09025 , 0.00000 , 0.98100 | 0.10352
+1.07870 | 1.07870 , 6.78618 , 1.00000 , 11.58209 | 0.97870 , 5.67702 , 1.00000 , 10.60109 | 0.10000 , 1.10916 , 0.00000 , 0.98100 | 0.10354
+1.09765 | 1.09765 , 7.00735 , 1.00000 , 11.76793 | 0.99765 , 5.87961 , 1.00000 , 10.78693 | 0.10000 , 1.12774 , 0.00000 , 0.98100 | 0.10349
+1.11627 | 1.11627 , 7.22818 , 1.00000 , 11.95061 | 1.01627 , 6.08217 , 1.00000 , 10.96961 | 0.10000 , 1.14601 , 0.00000 , 0.98100 | 0.10341
+1.13458 | 1.13458 , 7.44867 , 1.00000 , 12.13024 | 1.03458 , 6.28469 , 1.00000 , 11.14924 | 0.10000 , 1.16397 , 0.00000 , 0.98100 | 0.10331
+1.15260 | 1.15260 , 7.66879 , 1.00000 , 12.30698 | 1.05260 , 6.48714 , 1.00000 , 11.32598 | 0.10000 , 1.18165 , 0.00000 , 0.98100 | 0.10322
+1.17033 | 1.17033 , 7.88857 , 1.00000 , 12.48094 | 1.07033 , 6.68953 , 1.00000 , 11.49994 | 0.10000 , 1.19904 , 0.00000 , 0.98100 | 0.10312
+1.18779 | 1.18779 , 8.10801 , 1.00000 , 12.65224 | 1.08779 , 6.89184 , 1.00000 , 11.67124 | 0.10000 , 1.21617 , 0.00000 , 0.98100 | 0.10303
+1.20500 | 1.20500 , 8.32714 , 1.00000 , 12.82101 | 1.10500 , 7.09408 , 1.00000 , 11.84001 | 0.10000 , 1.23305 , 0.00000 , 0.98100 | 0.10294
+1.22195 | 1.22195 , 8.54595 , 1.00000 , 12.98736 | 1.12195 , 7.29626 , 1.00000 , 12.00636 | 0.10000 , 1.24969 , 0.00000 , 0.98100 | 0.10285
+1.23867 | 1.23867 , 8.76447 , 1.00000 , 13.15138 | 1.13867 , 7.49838 , 1.00000 , 12.17038 | 0.10000 , 1.26609 , 0.00000 , 0.98100 | 0.10277
+1.25517 | 1.25517 , 8.98271 , 1.00000 , 13.31318 | 1.15517 , 7.70044 , 1.00000 , 12.33218 | 0.10000 , 1.28227 , 0.00000 , 0.98100 | 0.10270
+1.27144 | 1.27144 , 9.20068 , 1.00000 , 13.47284 | 1.17144 , 7.90245 , 1.00000 , 12.49184 | 0.10000 , 1.29823 , 0.00000 , 0.98100 | 0.10263
+1.28751 | 1.28751 , 9.41839 , 1.00000 , 13.63044 | 1.18751 , 8.10440 , 1.00000 , 12.64944 | 0.10000 , 1.31399 , 0.00000 , 0.98100 | 0.10256
+1.30337 | 1.30337 , 9.63585 , 1.00000 , 13.78606 | 1.20337 , 8.30630 , 1.00000 , 12.80506 | 0.10000 , 1.32956 , 0.00000 , 0.98100 | 0.10249
+1.31904 | 1.31904 , 9.85308 , 1.00000 , 13.93978 | 1.21904 , 8.50815 , 1.00000 , 12.95878 | 0.10000 , 1.34493 , 0.00000 , 0.98100 | 0.10243
+1.33452 | 1.33452 , 10.07008 , 1.00000 , 14.09166 | 1.23452 , 8.70996 , 1.00000 , 13.11066 | 0.10000 , 1.36012 , 0.00000 , 0.98100 | 0.10237
+1.34982 | 1.34982 , 10.28685 , 1.00000 , 14.24177 | 1.24982 , 8.91173 , 1.00000 , 13.26077 | 0.10000 , 1.37513 , 0.00000 , 0.98100 | 0.10232
+1.36495 | 1.36495 , 10.50342 , 1.00000 , 14.39017 | 1.26495 , 9.11345 , 1.00000 , 13.40917 | 0.10000 , 1.38997 , 0.00000 , 0.98100 | 0.10227
+1.37991 | 1.37991 , 10.71978 , 1.00000 , 14.53692 | 1.27991 , 9.31513 , 1.00000 , 13.55592 | 0.10000 , 1.40464 , 0.00000 , 0.98100 | 0.10221
+1.39471 | 1.39471 , 10.93594 , 1.00000 , 14.68207 | 1.29471 , 9.51678 , 1.00000 , 13.70107 | 0.10000 , 1.41916 , 0.00000 , 0.98100 | 0.10217
+1.40934 | 1.40934 , 11.15191 , 1.00000 , 14.82567 | 1.30934 , 9.71839 , 1.00000 , 13.84467 | 0.10000 , 1.43352 , 0.00000 , 0.98100 | 0.10212
+1.42383 | 1.42383 , 11.36770 , 1.00000 , 14.96777 | 1.32383 , 9.91997 , 1.00000 , 13.98677 | 0.10000 , 1.44773 , 0.00000 , 0.98100 | 0.10208
+1.43817 | 1.43817 , 11.58331 , 1.00000 , 15.10843 | 1.33817 , 10.12152 , 1.00000 , 14.12743 | 0.10000 , 1.46179 , 0.00000 , 0.98100 | 0.10203
+1.45236 | 1.45236 , 11.79875 , 1.00000 , 15.24767 | 1.35236 , 10.32303 , 1.00000 , 14.26667 | 0.10000 , 1.47572 , 0.00000 , 0.98100 | 0.10199
+1.46642 | 1.46642 , 12.01402 , 1.00000 , 15.38555 | 1.36642 , 10.52451 , 1.00000 , 14.40455 | 0.10000 , 1.48950 , 0.00000 , 0.98100 | 0.10195
+1.48034 | 1.48034 , 12.22913 , 1.00000 , 15.52210 | 1.38034 , 10.72597 , 1.00000 , 14.54110 | 0.10000 , 1.50316 , 0.00000 , 0.98100 | 0.10192
+1.49412 | 1.49412 , 12.44408 , 1.00000 , 15.65736 | 1.39412 , 10.92740 , 1.00000 , 14.67636 | 0.10000 , 1.51669 , 0.00000 , 0.98100 | 0.10188
+1.50778 | 1.50778 , 12.65888 , 1.00000 , 15.79137 | 1.40778 , 11.12879 , 1.00000 , 14.81037 | 0.10000 , 1.53009 , 0.00000 , 0.98100 | 0.10184
+1.52132 | 1.52132 , 12.87353 , 1.00000 , 15.92416 | 1.42132 , 11.33017 , 1.00000 , 14.94316 | 0.10000 , 1.54337 , 0.00000 , 0.98100 | 0.10181
+1.53474 | 1.53474 , 13.08804 , 1.00000 , 16.05576 | 1.43474 , 11.53152 , 1.00000 , 15.07476 | 0.10000 , 1.55653 , 0.00000 , 0.98100 | 0.10178
+1.54803 | 1.54803 , 13.30241 , 1.00000 , 16.18621 | 1.44803 , 11.73284 , 1.00000 , 15.20521 | 0.10000 , 1.56957 , 0.00000 , 0.98100 | 0.10175
+1.56122 | 1.56122 , 13.51665 , 1.00000 , 16.31553 | 1.46122 , 11.93414 , 1.00000 , 15.33453 | 0.10000 , 1.58250 , 0.00000 , 0.98100 | 0.10172
+1.57429 | 1.57429 , 13.73075 , 1.00000 , 16.44376 | 1.47429 , 12.13542 , 1.00000 , 15.46276 | 0.10000 , 1.59533 , 0.00000 , 0.98100 | 0.10169
+1.58725 | 1.58725 , 13.94472 , 1.00000 , 16.57092 | 1.48725 , 12.33668 , 1.00000 , 15.58992 | 0.10000 , 1.60804 , 0.00000 , 0.98100 | 0.10166
+1.60011 | 1.60011 , 14.15857 , 1.00000 , 16.69704 | 1.50011 , 12.53792 , 1.00000 , 15.71604 | 0.10000 , 1.62065 , 0.00000 , 0.98100 | 0.10163
+1.61286 | 1.61286 , 14.37230 , 1.00000 , 16.82214 | 1.51286 , 12.73913 , 1.00000 , 15.84114 | 0.10000 , 1.63316 , 0.00000 , 0.98100 | 0.10161
+1.62551 | 1.62551 , 14.58591 , 1.00000 , 16.94625 | 1.52551 , 12.94033 , 1.00000 , 15.96525 | 0.10000 , 1.64558 , 0.00000 , 0.98100 | 0.10158
+1.63806 | 1.63806 , 14.79940 , 1.00000 , 17.06939 | 1.53806 , 13.14151 , 1.00000 , 16.08839 | 0.10000 , 1.65789 , 0.00000 , 0.98100 | 0.10156
+1.65052 | 1.65052 , 15.01278 , 1.00000 , 17.19159 | 1.55052 , 13.34267 , 1.00000 , 16.21059 | 0.10000 , 1.67011 , 0.00000 , 0.98100 | 0.10153
+1.66288 | 1.66288 , 15.22605 , 1.00000 , 17.31286 | 1.56288 , 13.54381 , 1.00000 , 16.33186 | 0.10000 , 1.68224 , 0.00000 , 0.98100 | 0.10151
+1.67515 | 1.67515 , 15.43921 , 1.00000 , 17.43322 | 1.57515 , 13.74494 , 1.00000 , 16.45222 | 0.10000 , 1.69427 , 0.00000 , 0.98100 | 0.10149
+1.68733 | 1.68733 , 15.65226 , 1.00000 , 17.55270 | 1.58733 , 13.94604 , 1.00000 , 16.57170 | 0.10000 , 1.70622 , 0.00000 , 0.98100 | 0.10146
+1.69942 | 1.69942 , 15.86522 , 1.00000 , 17.67132 | 1.59942 , 14.14714 , 1.00000 , 16.69032 | 0.10000 , 1.71808 , 0.00000 , 0.98100 | 0.10144
+1.71143 | 1.71143 , 16.07807 , 1.00000 , 17.78909 | 1.61143 , 14.34821 , 1.00000 , 16.80809 | 0.10000 , 1.72986 , 0.00000 , 0.98100 | 0.10142
+1.72335 | 1.72335 , 16.29083 , 1.00000 , 17.90603 | 1.62335 , 14.54927 , 1.00000 , 16.92503 | 0.10000 , 1.74155 , 0.00000 , 0.98100 | 0.10140
+1.73518 | 1.73518 , 16.50349 , 1.00000 , 18.02216 | 1.63518 , 14.75032 , 1.00000 , 17.04116 | 0.10000 , 1.75317 , 0.00000 , 0.98100 | 0.10138
+1.74694 | 1.74694 , 16.71605 , 1.00000 , 18.13750 | 1.64694 , 14.95135 , 1.00000 , 17.15650 | 0.10000 , 1.76470 , 0.00000 , 0.98100 | 0.10136
+1.75862 | 1.75862 , 16.92852 , 1.00000 , 18.25206 | 1.65862 , 15.15237 , 1.00000 , 17.27106 | 0.10000 , 1.77616 , 0.00000 , 0.98100 | 0.10134
+1.77022 | 1.77022 , 17.14091 , 1.00000 , 18.36585 | 1.67022 , 15.35337 , 1.00000 , 17.38485 | 0.10000 , 1.78754 , 0.00000 , 0.98100 | 0.10133
+1.78174 | 1.78174 , 17.35320 , 1.00000 , 18.47890 | 1.68174 , 15.55436 , 1.00000 , 17.49790 | 0.10000 , 1.79884 , 0.00000 , 0.98100 | 0.10131
+1.79319 | 1.79319 , 17.56541 , 1.00000 , 18.59122 | 1.69319 , 15.75534 , 1.00000 , 17.61022 | 0.10000 , 1.81007 , 0.00000 , 0.98100 | 0.10129
+1.80457 | 1.80457 , 17.77754 , 1.00000 , 18.70281 | 1.70457 , 15.95630 , 1.00000 , 17.72181 | 0.10000 , 1.82123 , 0.00000 , 0.98100 | 0.10128
+1.81587 | 1.81587 , 17.98958 , 1.00000 , 18.81370 | 1.71587 , 16.15726 , 1.00000 , 17.83270 | 0.10000 , 1.83232 , 0.00000 , 0.98100 | 0.10126
+1.82711 | 1.82711 , 18.20154 , 1.00000 , 18.92390 | 1.72711 , 16.35820 , 1.00000 , 17.94290 | 0.10000 , 1.84334 , 0.00000 , 0.98100 | 0.10124
+1.83827 | 1.83827 , 18.41342 , 1.00000 , 19.03342 | 1.73827 , 16.55913 , 1.00000 , 18.05242 | 0.10000 , 1.85429 , 0.00000 , 0.98100 | 0.10123
+1.84937 | 1.84937 , 18.62522 , 1.00000 , 19.14228 | 1.74937 , 16.76004 , 1.00000 , 18.16128 | 0.10000 , 1.86518 , 0.00000 , 0.98100 | 0.10121
+1.86040 | 1.86040 , 18.83695 , 1.00000 , 19.25048 | 1.76040 , 16.96095 , 1.00000 , 18.26948 | 0.10000 , 1.87600 , 0.00000 , 0.98100 | 0.10120
+1.87136 | 1.87136 , 19.04860 , 1.00000 , 19.35803 | 1.77136 , 17.16184 , 1.00000 , 18.37703 | 0.10000 , 1.88675 , 0.00000 , 0.98100 | 0.10118
+1.88226 | 1.88226 , 19.26017 , 1.00000 , 19.46496 | 1.78226 , 17.36273 , 1.00000 , 18.48396 | 0.10000 , 1.89745 , 0.00000 , 0.98100 | 0.10117
+1.89310 | 1.89310 , 19.47168 , 1.00000 , 19.57126 | 1.79310 , 17.56360 , 1.00000 , 18.59026 | 0.10000 , 1.90808 , 0.00000 , 0.98100 | 0.10116
+1.90387 | 1.90387 , 19.68311 , 1.00000 , 19.67696 | 1.80387 , 17.76447 , 1.00000 , 18.69596 | 0.10000 , 1.91865 , 0.00000 , 0.98100 | 0.10114
+1.91458 | 1.91458 , 19.89448 , 1.00000 , 19.78205 | 1.81458 , 17.96532 , 1.00000 , 18.80105 | 0.10000 , 1.92916 , 0.00000 , 0.98100 | 0.10113
+1.92524 | 1.92524 , 20.10577 , 1.00000 , 19.88656 | 1.82524 , 18.16617 , 1.00000 , 18.90556 | 0.10000 , 1.93961 , 0.00000 , 0.98100 | 0.10112
+1.93583 | 1.93583 , 20.31700 , 1.00000 , 19.99049 | 1.83583 , 18.36700 , 1.00000 , 19.00949 | 0.10000 , 1.95000 , 0.00000 , 0.98100 | 0.10111
+1.94637 | 1.94637 , 20.52816 , 1.00000 , 20.09384 | 1.84637 , 18.56783 , 1.00000 , 19.11284 | 0.10000 , 1.96033 , 0.00000 , 0.98100 | 0.10109
+1.95684 | 1.95684 , 20.73926 , 1.00000 , 20.19664 | 1.85684 , 18.76864 , 1.00000 , 19.21564 | 0.10000 , 1.97061 , 0.00000 , 0.98100 | 0.10108
+1.96727 | 1.96727 , 20.95029 , 1.00000 , 20.29888 | 1.86727 , 18.96945 , 1.00000 , 19.31788 | 0.10000 , 1.98084 , 0.00000 , 0.98100 | 0.10107
+1.97763 | 1.97763 , 21.16126 , 1.00000 , 20.40059 | 1.87763 , 19.17025 , 1.00000 , 19.41959 | 0.10000 , 1.99101 , 0.00000 , 0.98100 | 0.10106
+1.98795 | 1.98795 , 21.37217 , 1.00000 , 20.50175 | 1.88795 , 19.37104 , 1.00000 , 19.52075 | 0.10000 , 2.00113 , 0.00000 , 0.98100 | 0.10105
+1.99821 | 1.99821 , 21.58301 , 1.00000 , 20.60240 | 1.89821 , 19.57182 , 1.00000 , 19.62140 | 0.10000 , 2.01119 , 0.00000 , 0.98100 | 0.10104
+2.00841 | 2.00841 , 21.79380 , 1.00000 , 20.70252 | 1.90841 , 19.77260 , 1.00000 , 19.72152 | 0.10000 , 2.02120 , 0.00000 , 0.98100 | NaN
diff --git a/data_2D-Runge-Kutta-Fixed.txt b/data_2D-Runge-Kutta-Fixed.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9e0d5526ec51440dea41324655dfd72d9e0bcbcb
--- /dev/null
+++ b/data_2D-Runge-Kutta-Fixed.txt
@@ -0,0 +1,21 @@
+h | exact | result | error | error_estimated
+0.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 1.00000 , 1.00000 | 0.00000 , 0.00000 , 0.00000 , 0.00000 | NaN
+0.20000 | 0.20000 , 0.39620 , 1.00000 , 2.96200 | 0.10000 , 0.14905 , 1.00000 , 1.98100 | 0.10000 , 0.24715 , 0.00000 , 0.98100 | NaN
+0.30000 | 0.30000 , 0.74145 , 1.00000 , 3.94300 | 0.20000 , 0.39620 , 1.00000 , 2.96200 | 0.10000 , 0.34525 , 0.00000 , 0.98100 | NaN
+0.40000 | 0.40000 , 1.18480 , 1.00000 , 4.92400 | 0.30000 , 0.74145 , 1.00000 , 3.94300 | 0.10000 , 0.44335 , 0.00000 , 0.98100 | NaN
+0.50000 | 0.50000 , 1.72625 , 1.00000 , 5.90500 | 0.40000 , 1.18480 , 1.00000 , 4.92400 | 0.10000 , 0.54145 , 0.00000 , 0.98100 | NaN
+0.60000 | 0.60000 , 2.36580 , 1.00000 , 6.88600 | 0.50000 , 1.72625 , 1.00000 , 5.90500 | 0.10000 , 0.63955 , 0.00000 , 0.98100 | NaN
+0.70000 | 0.70000 , 3.10345 , 1.00000 , 7.86700 | 0.60000 , 2.36580 , 1.00000 , 6.88600 | 0.10000 , 0.73765 , 0.00000 , 0.98100 | NaN
+0.80000 | 0.80000 , 3.93920 , 1.00000 , 8.84800 | 0.70000 , 3.10345 , 1.00000 , 7.86700 | 0.10000 , 0.83575 , 0.00000 , 0.98100 | NaN
+0.90000 | 0.90000 , 4.87305 , 1.00000 , 9.82900 | 0.80000 , 3.93920 , 1.00000 , 8.84800 | 0.10000 , 0.93385 , 0.00000 , 0.98100 | NaN
+1.00000 | 1.00000 , 5.90500 , 1.00000 , 10.81000 | 0.90000 , 4.87305 , 1.00000 , 9.82900 | 0.10000 , 1.03195 , 0.00000 , 0.98100 | NaN
+1.10000 | 1.10000 , 7.03505 , 1.00000 , 11.79100 | 1.00000 , 5.90500 , 1.00000 , 10.81000 | 0.10000 , 1.13005 , 0.00000 , 0.98100 | NaN
+1.20000 | 1.20000 , 8.26320 , 1.00000 , 12.77200 | 1.10000 , 7.03505 , 1.00000 , 11.79100 | 0.10000 , 1.22815 , 0.00000 , 0.98100 | NaN
+1.30000 | 1.30000 , 9.58945 , 1.00000 , 13.75300 | 1.20000 , 8.26320 , 1.00000 , 12.77200 | 0.10000 , 1.32625 , 0.00000 , 0.98100 | NaN
+1.40000 | 1.40000 , 11.01380 , 1.00000 , 14.73400 | 1.30000 , 9.58945 , 1.00000 , 13.75300 | 0.10000 , 1.42435 , 0.00000 , 0.98100 | NaN
+1.50000 | 1.50000 , 12.53625 , 1.00000 , 15.71500 | 1.40000 , 11.01380 , 1.00000 , 14.73400 | 0.10000 , 1.52245 , 0.00000 , 0.98100 | NaN
+1.60000 | 1.60000 , 14.15680 , 1.00000 , 16.69600 | 1.50000 , 12.53625 , 1.00000 , 15.71500 | 0.10000 , 1.62055 , 0.00000 , 0.98100 | NaN
+1.70000 | 1.70000 , 15.87545 , 1.00000 , 17.67700 | 1.60000 , 14.15680 , 1.00000 , 16.69600 | 0.10000 , 1.71865 , 0.00000 , 0.98100 | NaN
+1.80000 | 1.80000 , 17.69220 , 1.00000 , 18.65800 | 1.70000 , 15.87545 , 1.00000 , 17.67700 | 0.10000 , 1.81675 , 0.00000 , 0.98100 | NaN
+1.90000 | 1.90000 , 19.60705 , 1.00000 , 19.63900 | 1.80000 , 17.69220 , 1.00000 , 18.65800 | 0.10000 , 1.91485 , 0.00000 , 0.98100 | NaN
+2.00000 | 2.00000 , 21.62000 , 1.00000 , 20.62000 | 1.90000 , 19.60705 , 1.00000 , 19.63900 | 0.10000 , 2.01295 , 0.00000 , 0.98100 | NaN
diff --git a/data_Euler-Adaptive.txt b/data_Euler-Adaptive.txt
new file mode 100644
index 0000000000000000000000000000000000000000..97027357691b2e574bc1e75c4f205feeb8d4e6ba
--- /dev/null
+++ b/data_Euler-Adaptive.txt
@@ -0,0 +1,10 @@
+h | exact | result | error | error_estimated
+0.0000000000 | 2.0000000000 | 2.0000000000 | 0.0000000000 | 0.0500000000
+0.2414213562 | 1.7725806914 | 1.8585786438 | 0.0859979524 | 0.0657106781
+0.4158818203 | 1.6245100627 | 1.6964543974 | 0.0719443348 | 0.0739910554
+0.6187002483 | 1.4678475212 | 1.5244182903 | 0.0565707692 | 0.0772950303
+0.8493917661 | 1.3079372756 | 1.3485831058 | 0.0406458301 | 0.0777766709
+1.1109732213 | 1.1475859589 | 1.1722009401 | 0.0246149812 | 0.0766565069
+1.4097400923 | 0.9883455795 | 0.9970935366 | 0.0087479571 | 0.0744746290
+1.7559410497 | 0.8312511161 | 0.8244961681 | 0.0067549480 | 0.0713603407
+2.1657673327 | 0.6772353121 | 0.6555460682 | 0.0216892439 | NaN
diff --git a/data_Euler-Fixed.txt b/data_Euler-Fixed.txt
new file mode 100644
index 0000000000000000000000000000000000000000..51cd372dfa01162637cd5e5a5637fa3231c9365c
--- /dev/null
+++ b/data_Euler-Fixed.txt
@@ -0,0 +1,21 @@
+h | exact | result | error | error_estimated
+0.0000000000 | 2.0000000000 | 2.0000000000 | 0.0000000000 | NaN
+0.2000000000 | 1.8096748361 | 1.9000000000 | 0.0903251639 | NaN
+0.3000000000 | 1.7214159529 | 1.8050000000 | 0.0835840471 | NaN
+0.4000000000 | 1.6374615062 | 1.7147500000 | 0.0772884938 | NaN
+0.5000000000 | 1.5576015661 | 1.6290125000 | 0.0714109339 | NaN
+0.6000000000 | 1.4816364414 | 1.5475618750 | 0.0659254336 | NaN
+0.7000000000 | 1.4093761794 | 1.4701837813 | 0.0608076018 | NaN
+0.8000000000 | 1.3406400921 | 1.3966745922 | 0.0560345001 | NaN
+0.9000000000 | 1.2752563032 | 1.3268408626 | 0.0515845593 | NaN
+1.0000000000 | 1.2130613194 | 1.2604988194 | 0.0474375000 | NaN
+1.1000000000 | 1.1538996208 | 1.1974738785 | 0.0435742577 | NaN
+1.2000000000 | 1.0976232722 | 1.1376001846 | 0.0399769124 | NaN
+1.3000000000 | 1.0440915535 | 1.0807201753 | 0.0366286218 | NaN
+1.4000000000 | 0.9931706076 | 1.0266841666 | 0.0335135590 | NaN
+1.5000000000 | 0.9447331055 | 0.9753499582 | 0.0306168527 | NaN
+1.6000000000 | 0.8986579282 | 0.9265824603 | 0.0279245321 | NaN
+1.7000000000 | 0.8548298639 | 0.8802533373 | 0.0254234734 | NaN
+1.8000000000 | 0.8131393195 | 0.8362406704 | 0.0231013510 | NaN
+1.9000000000 | 0.7734820469 | 0.7944286369 | 0.0209465900 | NaN
+2.0000000000 | 0.7357588823 | 0.7547072051 | 0.0189483227 | NaN
diff --git a/data_Midpoint-Adaptive.txt b/data_Midpoint-Adaptive.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4910caf6991b4c472fe0f9062eeb4609628fc0f6
--- /dev/null
+++ b/data_Midpoint-Adaptive.txt
@@ -0,0 +1,10 @@
+h | exact | result | error | error_estimated
+0.0000000000 | 2.0000000000 | 2.0000000000 | 0.0000000000 | 0.0481250000
+0.2441499940 | 1.7701639750 | 1.8610448112 | 0.0908808362 | 0.0634419876
+0.4251281831 | 1.6170169922 | 1.7002599258 | 0.0832429336 | 0.0717066664
+0.6388488260 | 1.4531342386 | 1.5282773467 | 0.0751431080 | 0.0751117561
+0.8854485090 | 1.2845685793 | 1.3514580784 | 0.0668894991 | 0.0756125276
+1.1690415935 | 1.1147457855 | 1.1734123793 | 0.0586665938 | 0.0743455589
+1.4979448101 | 0.9457044074 | 0.9963099029 | 0.0506054955 | 0.0718181822
+1.8860513103 | 0.7788954329 | 0.8217315817 | 0.0428361488 | 0.0681259658
+2.3562642545 | 0.6157064651 | 0.6512477970 | 0.0355413319 | NaN
diff --git a/data_Midpoint-Fixed.txt b/data_Midpoint-Fixed.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9daaac29dc38fa084172da1da9308c76d975d84a
--- /dev/null
+++ b/data_Midpoint-Fixed.txt
@@ -0,0 +1,21 @@
+h | exact | result | error | error_estimated
+0.0000000000 | 2.0000000000 | 2.0000000000 | 0.0000000000 | NaN
+0.2000000000 | 1.8096748361 | 1.9025000000 | 0.0928251639 | NaN
+0.3000000000 | 1.7214159529 | 1.8097531250 | 0.0883371721 | NaN
+0.4000000000 | 1.6374615062 | 1.7215276602 | 0.0840661540 | NaN
+0.5000000000 | 1.5576015661 | 1.6376031867 | 0.0800016206 | NaN
+0.6000000000 | 1.4816364414 | 1.5577700314 | 0.0761335900 | NaN
+0.7000000000 | 1.4093761794 | 1.4818287423 | 0.0724525629 | NaN
+0.8000000000 | 1.3406400921 | 1.4095895912 | 0.0689494991 | NaN
+0.9000000000 | 1.2752563032 | 1.3408720986 | 0.0656157953 | NaN
+1.0000000000 | 1.2130613194 | 1.2755045838 | 0.0624432644 | NaN
+1.1000000000 | 1.1538996208 | 1.2133237353 | 0.0594241146 | NaN
+1.2000000000 | 1.0976232722 | 1.1541742032 | 0.0565509310 | NaN
+1.3000000000 | 1.0440915535 | 1.0979082108 | 0.0538166573 | NaN
+1.4000000000 | 0.9931706076 | 1.0443851855 | 0.0512145780 | NaN
+1.5000000000 | 0.9447331055 | 0.9934714077 | 0.0487383023 | NaN
+1.6000000000 | 0.8986579282 | 0.9450396766 | 0.0463817484 | NaN
+1.7000000000 | 0.8548298639 | 0.8989689924 | 0.0441391285 | NaN
+1.8000000000 | 0.8131393195 | 0.8551442540 | 0.0420049345 | NaN
+1.9000000000 | 0.7734820469 | 0.8134559716 | 0.0399739247 | NaN
+2.0000000000 | 0.7357588823 | 0.7737999930 | 0.0380411107 | NaN
diff --git a/data_Runge-Kutta-Adaptive.txt b/data_Runge-Kutta-Adaptive.txt
new file mode 100644
index 0000000000000000000000000000000000000000..31c59b37ce021c22a522b580eaf277e924d8ea72
--- /dev/null
+++ b/data_Runge-Kutta-Adaptive.txt
@@ -0,0 +1,10 @@
+h | exact | result | error | error_estimated
+0.0000000000 | 2.0000000000 | 2.0000000000 | 0.0000000000 | 0.0481609701
+0.2440961532 | 1.7702116292 | 1.8609723522 | 0.0907607230 | 0.0635167168
+0.4249002915 | 1.6172012550 | 1.7001170578 | 0.0829158029 | 0.0718154420
+0.6382536323 | 1.4535667512 | 1.5280930136 | 0.0745262624 | 0.0752476504
+0.8842071146 | 1.2853661550 | 1.3512689045 | 0.0659027495 | 0.0757783891
+1.1667473426 | 1.1160252724 | 1.1732462669 | 0.0572209944 | 0.0745559154
+1.4939668887 | 0.9475872482 | 0.9961731817 | 0.0485859336 | 0.0721005439
+1.8793298471 | 0.7815174949 | 0.8215906186 | 0.0400731237 | 0.0685270763
+2.3448504063 | 0.6192303008 | 0.6509864814 | 0.0317561807 | NaN
diff --git a/data_Runge-Kutta-Fixed.txt b/data_Runge-Kutta-Fixed.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ce1978fd8f8b2c98ea886fc781345d93d2736913
--- /dev/null
+++ b/data_Runge-Kutta-Fixed.txt
@@ -0,0 +1,21 @@
+h | exact | result | error | error_estimated
+0.0000000000 | 2.0000000000 | 2.0000000000 | 0.0000000000 | NaN
+0.2000000000 | 1.8096748361 | 1.9024588542 | 0.0927840181 | NaN
+0.3000000000 | 1.7214159529 | 1.8096748459 | 0.0882588930 | NaN
+0.4000000000 | 1.6374615062 | 1.7214159669 | 0.0839544607 | NaN
+0.5000000000 | 1.5576015661 | 1.6374615239 | 0.0798599578 | NaN
+0.6000000000 | 1.4816364414 | 1.5576015873 | 0.0759651459 | NaN
+0.7000000000 | 1.4093761794 | 1.4816364655 | 0.0722602861 | NaN
+0.8000000000 | 1.3406400921 | 1.4093762062 | 0.0687361142 | NaN
+0.9000000000 | 1.2752563032 | 1.3406401212 | 0.0653838179 | NaN
+1.0000000000 | 1.2130613194 | 1.2752563344 | 0.0621950150 | NaN
+1.1000000000 | 1.1538996208 | 1.2130613524 | 0.0591617316 | NaN
+1.2000000000 | 1.0976232722 | 1.1538996552 | 0.0562763830 | NaN
+1.3000000000 | 1.0440915535 | 1.0976233079 | 0.0535317544 | NaN
+1.4000000000 | 0.9931706076 | 1.0440915904 | 0.0509209828 | NaN
+1.5000000000 | 0.9447331055 | 0.9931706453 | 0.0484375399 | NaN
+1.6000000000 | 0.8986579282 | 0.9447331440 | 0.0460752157 | NaN
+1.7000000000 | 0.8548298639 | 0.8986579673 | 0.0438281034 | NaN
+1.8000000000 | 0.8131393195 | 0.8548299034 | 0.0416905839 | NaN
+1.9000000000 | 0.7734820469 | 0.8131393592 | 0.0396573123 | NaN
+2.0000000000 | 0.7357588823 | 0.7734820868 | 0.0377232045 | NaN
diff --git a/src/init.ts b/src/init.ts
index 8e4444dc0a7b3a812aeca0663968175a9bf445d9..b1d7b1fbd36748405d54d3012d36f9fdb1519986 100644
--- a/src/init.ts
+++ b/src/init.ts
@@ -16,7 +16,6 @@ function init() {
const simulationLink = document.querySelector("#simulation") as HTMLAnchorElement;
// actions to be performed when the link is clicked
-
const bezierFunc = () => {
sceneElement.classList.remove("hidden");
mainElement.classList.add("hidden");
@@ -30,9 +29,9 @@ function init() {
};
const simulationFunc = () => {
- sceneElement.classList.add("hidden");
- mainElement.classList.remove("hidden");
- // TODO: add simulation
+ sceneElement.classList.remove("hidden");
+ mainElement.classList.add("hidden");
+ Main.demos(Main.examples["simulation"]);
};
bezierLink.addEventListener("click", bezierFunc);
diff --git a/src/main.ts b/src/main.ts
index bc571aa70262bbf886535f278ce6267d8bc8b81b..bd9088b15eaa5a36815792bd19a7fe1f83642eaf 100644
--- a/src/main.ts
+++ b/src/main.ts
@@ -3,6 +3,7 @@ import { UI } from "./uitls/UI";
import { bezierDemo } from "./bezier/BezierDemo";
import { quaternionDemo } from "./quaternion/QuaternionDemo";
+import { simulationDemo } from "./simulation/SimulationDemo";
/**
@@ -11,7 +12,8 @@ import { quaternionDemo } from "./quaternion/QuaternionDemo";
*/
export const examples : {[key: string]: (render: RenderManager, ui: UI) => void} = {
"bezier": bezierDemo,
- "quaternion": quaternionDemo
+ "quaternion": quaternionDemo,
+ "simulation": simulationDemo
};
diff --git a/src/quaternion/QuaternionDemo.ts b/src/quaternion/QuaternionDemo.ts
index 0c1eed622d54e124f75c314baa8fcf8583503f6d..86bcb044fa602217c0fed34fc5a92348a10564d6 100644
--- a/src/quaternion/QuaternionDemo.ts
+++ b/src/quaternion/QuaternionDemo.ts
@@ -4,8 +4,6 @@ import { UI } from "../uitls/UI";
import { AmbientLight, GridHelper, Mesh, MeshLambertMaterial, PointLight } from "three";
import { OBJLoader } from "three/examples/jsm/loaders/OBJLoader";
import { RotationObject } from "./RotationObject";
-
-
/**
* Prepares the scene for the demo.
*/
diff --git a/src/simulation/ClothSimulation.ts b/src/simulation/ClothSimulation.ts
new file mode 100644
index 0000000000000000000000000000000000000000..44c6a72afc4a0c0cb91112a413f7c54b5a8a7dd9
--- /dev/null
+++ b/src/simulation/ClothSimulation.ts
@@ -0,0 +1,128 @@
+import { GUI } from "dat.gui";
+import { Object3D, Vector3 } from "three";
+import { Animatable, Updatable, Modifiable } from "../uitls/Interfaces";
+import { Particle } from "./Particle";
+import { Spring } from "./Spring";
+import * as Integrator from "./Integrators";
+
+class PhysicsModel {
+ static gravity: Vector3 = new Vector3(0, -9.81, 0);
+ static particle: Particle;
+ static error_max: number = 0.000001;
+
+ static step(x: Array<number>): Array<number> {
+ // determine force
+ let f_accum = new Vector3(0, 0, 0);
+ for (let spring of PhysicsModel.particle.associatedSprings) {
+ f_accum.add(spring.getForce(PhysicsModel.particle));
+ }
+ console.log(f_accum);
+
+ // calculate current acceleration
+ let a = f_accum.divideScalar(Particle.mass);
+ a.add(new Vector3(PhysicsModel.gravity.x, PhysicsModel.gravity.y, PhysicsModel.gravity.z));
+ console.log(a);
+
+ // derivative for particles
+ return [x[3], x[4], x[5], a.x, a.y, a.z];
+ }
+}
+
+
+export class Simulator implements Animatable, Modifiable {
+
+ // create a grid of particles
+ public particles: Array<Array<Particle>>;
+ public springs: Array<Spring>;
+ private h: number = 1/60/10;
+
+ // width and height are in meters
+ constructor(width: number, height: number, numRow: number, numCol: number) {
+ this.particles = [];
+ this.springs = [];
+
+ // set particle radius
+ const radius = Math.min(width / numCol / 2, height / numRow / 2);
+
+ // create particles and
+ for (let i = 0; i < numRow; i++) {
+ this.particles[i] = [];
+ for (let j = 0; j < numCol; j++) {
+ const p = new Particle(new Vector3(i * width / (numRow - 1), j * height / (numCol - 1), 0), new Vector3(0, 0, 0), radius, (i == 0 && j == numCol - 1 || i == numRow - 1 && j == numCol - 1));
+ this.particles[i][j] = p;
+ }
+ }
+
+ // create springs
+ for (let i = 0; i < numRow; i++) {
+ for (let j = 0; j < numCol; j++) {
+
+ // 1. structural springs
+ if (0 < i) {
+ let spring = new Spring(this.particles[i][j], this.particles[i - 1][j], Spring.Type.STRUCTURAL);
+ this.springs.push(spring);
+ this.particles[i][j].associatedSprings.push(spring);
+ this.particles[i - 1][j].associatedSprings.push(spring);
+ }
+ if (0 < j) {
+ let spring = new Spring(this.particles[i][j], this.particles[i][j - 1], Spring.Type.STRUCTURAL);
+ this.springs.push(spring);
+ this.particles[i][j].associatedSprings.push(spring);
+ this.particles[i][j - 1].associatedSprings.push(spring);
+ }
+ }
+ }
+ }
+
+ public objects(): Object3D[] {
+ let objects: Object3D[] = [];
+
+ this.particles.forEach(row => {
+ row.forEach(particle => {
+ objects.push(particle.shape);
+ });
+ });
+
+ this.springs.forEach(spring => {
+ objects.push(spring.line);
+ });
+
+ return objects;
+ }
+
+ animate(delta: number) : void {
+ // iterate over all particles
+ for (let i = 0; i < this.particles.length; i++) {
+ for (let j = 0; j < this.particles[i].length; j++) {
+ const particle = this.particles[i][j];
+
+ if (particle.pinn)
+ continue;
+
+ PhysicsModel.particle = particle;
+
+ // build list
+ let particle_list: Array<number> = [
+ particle.position.x,
+ particle.position.y,
+ particle.position.z,
+ particle.velocity.x,
+ particle.velocity.y,
+ particle.velocity.z
+ ];
+
+ for(let i = 0; i < delta/60; i++) {
+ particle_list = Integrator.Euler(particle_list, this.h, PhysicsModel.step);
+ }
+
+ particle.update(new Vector3(particle_list[0], particle_list[1], particle_list[2])
+ , new Vector3(particle_list[3], particle_list[4], particle_list[5]));
+
+ }
+ }
+
+ }
+
+ createElement(gui: GUI): void {
+ }
+}
\ No newline at end of file
diff --git a/src/simulation/Particle.ts b/src/simulation/Particle.ts
new file mode 100644
index 0000000000000000000000000000000000000000..536e45ba97ddf01375a060ad19446732f3242b6b
--- /dev/null
+++ b/src/simulation/Particle.ts
@@ -0,0 +1,34 @@
+import { Vector3, Mesh, SphereBufferGeometry, MeshLambertMaterial } from "three";
+import { Spring } from "./Spring";
+
+
+export class Particle {
+
+ static mass = .01;
+
+ public position: Vector3;
+ public velocity: Vector3;
+
+ public pinn: boolean = false;
+ public shape: Mesh;
+ public associatedSprings: Spring[] = [];
+
+ constructor(position: Vector3, velocity: Vector3, radius: number = 0.1, pinned: boolean = false) {
+ this.position = position;
+ this.velocity = velocity;
+ this.pinn = pinned;
+ this.shape = new Mesh(new SphereBufferGeometry(radius), new MeshLambertMaterial({ color: (pinned) ? 0x664422 : 0xffffff }));
+ this.shape.position.copy(position);
+ }
+
+ public update(position: Vector3, velocity: Vector3) {
+ if (!this.pinn) {
+ this.position.copy(position);
+ this.velocity.copy(velocity);
+ this.shape.position.copy(this.position);
+ for (let spring of this.associatedSprings) {
+ spring.update();
+ }
+ }
+ }
+}
\ No newline at end of file
diff --git a/src/simulation/SimulationDemo.ts b/src/simulation/SimulationDemo.ts
new file mode 100644
index 0000000000000000000000000000000000000000..1af51f2d9f0afe4b763150e1d6a39486d5dae408
--- /dev/null
+++ b/src/simulation/SimulationDemo.ts
@@ -0,0 +1,29 @@
+import { AmbientLight, PointLight } from "three";
+import { RenderManager } from "../uitls/Rendering";
+import { UI } from "../uitls/UI";
+import { Simulator } from "./ClothSimulation";
+
+export function simulationDemo(render: RenderManager, ui: UI) {
+ const simulator = new Simulator(.20, .20, 2, 2);
+ simulator.objects().forEach(obj => {
+ render.add(obj);
+ });
+ ui.addModifiable(simulator);
+ render.simulator = simulator;
+
+ const ambient = new AmbientLight(0x404040);
+ render.add(ambient);
+
+ const plightx = new PointLight(0xffffff, 1, 100);
+ plightx.position.set(5, 0, 0);
+ render.add(plightx);
+
+ const plighty = new PointLight(0xffffff, 1, 100);
+ plighty.position.set(0, 5, 0);
+ render.add(plighty);
+
+ const plightz = new PointLight(0xffffff, 1, 100);
+ plightz.position.set(0, 0, 5);
+ render.add(plightz);
+
+}
\ No newline at end of file
diff --git a/src/simulation/Spring.ts b/src/simulation/Spring.ts
new file mode 100644
index 0000000000000000000000000000000000000000..2c04ccb2d25a86f50605a7b08b3c3bd07b500ba7
--- /dev/null
+++ b/src/simulation/Spring.ts
@@ -0,0 +1,62 @@
+import { Vector3, Line, LineBasicMaterial, BufferGeometry } from "three";
+import { Particle } from "./Particle";
+import { colorprime } from "../uitls/Globals";
+import { abs } from "mathjs";
+
+export class Spring {
+
+ static Type = {
+ STRUCTURAL: 0,
+ SHEAR: 1,
+ BEND: 2
+ };
+
+ public static kd: number = 0.80;
+
+ public start: Particle;
+ public end: Particle;
+
+ public restLength: Vector3;
+ public line: Line;
+
+ public type: number;
+
+ private offset: Vector3;
+
+ constructor(start: Particle, end: Particle, type: number) {
+ this.start = start;
+ this.end = end;
+ this.type = type;
+
+ if (type === Spring.Type.STRUCTURAL) {
+ this.offset = new Vector3(1e-4);
+ }
+ else {
+ this.offset = new Vector3(0, 0, 0);
+ }
+ this.restLength = new Vector3().subVectors(end.position, start.position);
+ this.line = new Line(undefined, new LineBasicMaterial({ color: Number(colorprime[type]) }));
+ this.line.geometry = new BufferGeometry().setFromPoints([this.start.position.clone().add(this.offset), this.end.position.clone().add(this.offset)]);
+ }
+
+ public getForce(p: Particle): Vector3 {
+ let distance = this.start.position.distanceTo(this.end.position);
+ let force = (abs(distance) - this.restLength.length()) * -Spring.kd * distance / abs(distance);
+
+ let direction = new Vector3().subVectors(this.start.position, this.end.position).normalize();
+ direction.multiplyScalar(force);
+
+ if (p !== this.start) {
+ return direction.multiplyScalar(-1);
+ }
+ else {
+ return direction;
+ }
+ }
+
+ public update() {
+ this.line.geometry.dispose();
+ this.line.geometry = new BufferGeometry().setFromPoints([this.start.position.clone().add(this.offset), this.end.position.clone().add(this.offset)]);
+ }
+}
+
diff --git a/src/uitls/rendering.ts b/src/uitls/rendering.ts
index 7183b023ac6852bfc871fa9e2afc7b241a14aad6..6b8884ee251127888b1d914dc81339695c09dc5d 100644
--- a/src/uitls/rendering.ts
+++ b/src/uitls/rendering.ts
@@ -2,8 +2,9 @@ import {
Camera, OrthographicCamera, PerspectiveCamera, WebGLRenderer, Object3D, Scene
} from 'three';
import { OrbitControls } from 'three/examples/jsm/controls/OrbitControls';
-import { Modifiable } from './Interfaces';
+import { Modifiable, Animatable } from './Interfaces';
import { GUI } from 'dat.gui';
+import { Simulator } from '../simulation/ClothSimulation';
export interface CameraSettings {
@@ -105,7 +106,6 @@ export class RenderManager implements Modifiable {
* Render routine (called by the main loop)
*/
render(): void {
-
// request frame
requestAnimationFrame(() => this.render());
@@ -115,6 +115,11 @@ export class RenderManager implements Modifiable {
// update if delta is greater than 1/60
if (delta > interval) {
+ // update animatables
+ if (this.simulator) {
+ this.simulator.animate(delta);
+ }
+
this._past = now - (delta % interval);
this._renderer.render(this._scene, this._cameraManager.camera());
this._controls.update();
@@ -122,7 +127,6 @@ export class RenderManager implements Modifiable {
}
-
/**
* Extends the scene with a new object from THREE.js
* @param object - the object to add to the scene
@@ -151,6 +155,7 @@ export class RenderManager implements Modifiable {
}
+ public simulator?: Simulator;
private _fps: number = 60;
private _controls: OrbitControls;
private _cameraManager: CameraManager;