Неявная схема

Линии уровня решения уравненияU(x,t), найденные с помощью явной схемы h=1/40

Решение уравнения U(x,t), найденного с помощью неявной разностной схемы (T-образный шаблон) на w={(x,y)/0<=x,y<=1}

Полученная матрица для N=20 M=20 (неявный метод)

u =

Columns 1 through 7 Columns 8 through 14

0 0.1004 -0.0232 -0.1023 -0.0861 -0.0410 -0.0167 -0.0121 -0.0087 0.0015 0.0148 0.0262 0.0347 0.0417

0.1564 0.1545 0.1381 0.0875 0.0460 0.0331 0.0337 0.0300 0.0189 0.0064 -0.0033 -0.0102 -0.0157 -0.0206

0.3090 0.3017 0.2825 0.2406 0.1846 0.1333 0.0951 0.0652 0.0367 0.0073 -0.0212 -0.0463 -0.0674 -0.0846

0.4540 0.4393 0.4126 0.3685 0.3066 0.2357 0.1671 0.1065 0.0533 0.0047 -0.0405 -0.0816 -0.1174 -0.1473

0.5878 0.5645 0.5281 0.4765 0.4084 0.3266 0.2388 0.1532 0.0747 0.0043 -0.0589 -0.1153 -0.1647 -0.2066

0.7071 0.6747 0.6279 0.5669 0.4910 0.4014 0.3021 0.1997 0.1007 0.0094 -0.0725 -0.1447 -0.2076 -0.2608

0.8090 0.7676 0.7110 0.6403 0.5564 0.4599 0.3532 0.2405 0.1276 0.0198 -0.0791 -0.1671 -0.2435 -0.3080

0.8910 0.8416 0.7764 0.6973 0.6059 0.5034 0.3915 0.2729 0.1517 0.0327 -0.0794 -0.1811 -0.2703 -0.3458

0.9511 0.8954 0.8235 0.7378 0.6406 0.5334 0.4180 0.2961 0.1707 0.0454 -0.0752 -0.1872 -0.2870 -0.3724

0.9877 0.9280 0.8519 0.7621 0.6611 0.5510 0.4336 0.3104 0.1836 0.0559 -0.0690 -0.1870 -0.2941 -0.3870

1.0000 0.9389 0.8614 0.7702 0.6680 0.5571 0.4393 0.3165 0.1903 0.0629 -0.0625 -0.1825 -0.2929 -0.3900

0.9877 0.9280 0.8519 0.7622 0.6614 0.5519 0.4358 0.3149 0.1911 0.0664 -0.0567 -0.1749 -0.2846 -0.3821

0.9511 0.8954 0.8235 0.7380 0.6412 0.5355 0.4231 0.3061 0.1865 0.0664 -0.0516 -0.1649 -0.2703 -0.3646

0.8910 0.8416 0.7764 0.6976 0.6073 0.5077 0.4012 0.2901 0.1768 0.0636 -0.0471 -0.1527 -0.2507 -0.3385

0.8090 0.7676 0.7111 0.6410 0.5594 0.4682 0.3699 0.2671 0.1623 0.0583 -0.0425 -0.1379 -0.2260 -0.3046

0.7071 0.6747 0.6281 0.5685 0.4974 0.4167 0.3289 0.2369 0.1435 0.0514 -0.0372 -0.1203 -0.1963 -0.2640

0.5878 0.5645 0.5286 0.4805 0.4213 0.3531 0.2784 0.2000 0.1208 0.0431 -0.0309 -0.0997 -0.1621 -0.2174

0.4540 0.4393 0.4139 0.3777 0.3317 0.2780 0.2189 0.1570 0.0947 0.0340 -0.0234 -0.0763 -0.1241 -0.1661

0.3090 0.3017 0.2859 0.2616 0.2299 0.1925 0.1515 0.1086 0.0657 0.0241 -0.0151 -0.0511 -0.0834 -0.1116

0.1564 0.1545 0.1470 0.1345 0.1182 0.0989 0.0779 0.0560 0.0341 0.0129 -0.0070 -0.0251 -0.0414 -0.0556

0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0

Columns 15 through 21

0.0480 0.0538 0.0585 0.0620 0.0643 0.0657 0.0660

-0.0244 -0.0268 -0.0276 -0.0271 -0.0252 -0.0221 -0.0175

-0.0983 -0.1084 -0.1148 -0.1173 -0.1160 -0.1110 -0.1022

-0.1712 -0.1889 -0.2006 -0.2062 -0.2055 -0.1986 -0.1856

-0.2404 -0.2659 -0.2829 -0.2914 -0.2912 -0.2825 -0.2654

-0.3041 -0.3370 -0.3592 -0.3705 -0.3709 -0.3604 -0.3392

-0.3604 -0.4003 -0.4273 -0.4413 -0.4421 -0.4298 -0.4050

-0.4070 -0.4536 -0.4851 -0.5014 -0.5026 -0.4888 -0.4607

-0.4419 -0.4947 -0.5304 -0.5489 -0.5504 -0.5354 -0.5046

-0.4633 -0.5216 -0.5610 -0.5816 -0.5837 -0.5679 -0.5353

-0.4707 -0.5329 -0.5755 -0.5980 -0.6009 -0.5851 -0.5518

-0.4642 -0.5282 -0.5727 -0.5969 -0.6011 -0.5861 -0.5532

-0.4447 -0.5081 -0.5528 -0.5780 -0.5837 -0.5703 -0.5392

-0.4135 -0.4736 -0.5168 -0.5422 -0.5492 -0.5381 -0.5100

-0.3721 -0.4266 -0.4666 -0.4909 -0.4988 -0.4904 -0.4661

-0.3220 -0.3692 -0.4043 -0.4264 -0.4347 -0.4288 -0.4088

-0.2647 -0.3034 -0.3325 -0.3514 -0.3592 -0.3554 -0.3399

-0.2020 -0.2314 -0.2538 -0.2686 -0.2752 -0.2730 -0.2618

-0.1357 -0.1554 -0.1705 -0.1807 -0.1854 -0.1844 -0.1772

-0.0676 -0.0775 -0.0851 -0.0903 -0.0928 -0.0924 -0.0889

0 0 0 0 0 0 0