Результаты работы.

Явная схема.

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

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

Полученная матрица для N=20 M=21 (явный метод)

u =

Columns 1 through 7 Columns 8 through 14

0 -0.0001 -0.0005 -0.0015 -0.0033 -0.0062 -0.0104 - 0.0162 -0.0239 -0.0337 -0.0461 -0.0614 -0.0799 -0.1019

0.1564 0.1547 0.1486 0.1369 0.1202 0.0990 0.0740 0.0460 0.0158 -0.0159 -0.0486 -0.0819 -0.1155 -0.1496

0.3090 0.3022 0.2890 0.2673 0.2363 0.1975 0.1526 0.1033 0.0513 -0.0016 -0.0542 -0.1053 -0.1542 -0.2005

0.4540 0.4402 0.4175 0.3849 0.3413 0.2868 0.2238 0.1551 0.0832 0.0106 -0.0607 -0.1288 -0.1925 -0.2513

0.5878 0.5659 0.5327 0.4879 0.4318 0.3643 0.2862 0.2009 0.1118 0.0218 -0.0662 -0.1500 -0.2279 -0.2988

0.7071 0.6765 0.6326 0.5759 0.5072 0.4277 0.3381 0.2400 0.1369 0.0328 -0.0695 -0.1672 -0.2580 -0.3408

0.8090 0.7699 0.7159 0.6482 0.5681 0.4775 0.3781 0.2711 0.1583 0.0433 -0.0702 -0.1794 -0.2817 -0.3754

0.8910 0.8444 0.7816 0.7044 0.6149 0.5151 0.4072 0.2933 0.1747 0.0530 -0.0687 -0.1866 -0.2984 -0.4017

0.9511 0.8985 0.8289 0.7446 0.6479 0.5413 0.4273 0.3079 0.1851 0.0603 -0.0655 -0.1895 -0.3082 -0.4198

0.9877 0.9313 0.8575 0.7686 0.6675 0.5567 0.4389 0.3162 0.1907 0.0640 -0.0628 -0.1891 -0.3127 -0.4307

1.0000 0.9423 0.8670 0.7766 0.6740 0.5618 0.4427 0.3190 0.1925 0.0651 -0.0620 -0.1882 -0.3135 -0.4341

0.9877 0.9313 0.8575 0.7686 0.6675 0.5567 0.4389 0.3162 0.1907 0.0640 -0.0628 -0.1888 -0.3117 -0.4286

0.9511 0.8985 0.8289 0.7446 0.6479 0.5413 0.4273 0.3079 0.1851 0.0604 -0.0652 -0.1884 -0.3057 -0.4149

0.8910 0.8444 0.7816 0.7044 0.6149 0.5151 0.4072 0.2933 0.1748 0.0533 -0.0676 -0.1840 -0.2933 -0.3930

0.8090 0.7699 0.7159 0.6482 0.5681 0.4775 0.3781 0.2712 0.1587 0.0444 -0.0675 -0.1742 -0.2728 -0.3611

0.7071 0.6765 0.6326 0.5759 0.5072 0.4277 0.3382 0.2404 0.1382 0.0356 -0.0642 -0.1579 -0.2435 -0.3190

0.5878 0.5659 0.5327 0.4879 0.4318 0.3643 0.2866 0.2022 0.1147 0.0274 -0.0567 -0.1351 -0.2057 -0.2672

0.4540 0.4402 0.4175 0.3849 0.3414 0.2872 0.2252 0.1582 0.0889 0.0203 -0.0455 -0.1062 -0.1604 -0.2072

0.3090 0.3022 0.2890 0.2674 0.2367 0.1989 0.1557 0.1091 0.0612 0.0139 -0.0312 -0.0726 -0.1094 -0.1408

0.1564 0.1547 0.1487 0.1374 0.1217 0.1022 0.0800 0.0562 0.0317 0.0075 -0.0154 -0.0364 -0.0550 -0.0708

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

Columns 15 through 21 Column 22

-0.1279 -0.1583 -0.1935 -0.2339 -0.2801 -0.3324 -0.3914 -0.4577

-0.1844 -0.2202 -0.2577 -0.2976 -0.3406 -0.3875 -0.4393 -0.4970

-0.2445 -0.2864 -0.3270 -0.3672 -0.4079 -0.4504 -0.4962 -0.5456

-0.3049 -0.3536 -0.3983 -0.4399 -0.4797 -0.5194 -0.5597 -0.5992

-0.3624 -0.4189 -0.4687 -0.5132 -0.5539 -0.5915 -0.6249 -0.6531

-0.4146 -0.4793 -0.5357 -0.5849 -0.6272 -0.6614 -0.6869 -0.7039

-0.4593 -0.5330 -0.5973 -0.6515 -0.6940 -0.7242 -0.7420 -0.7478

-0.4953 -0.5787 -0.6503 -0.7077 -0.7497 -0.7759 -0.7864 -0.7820

-0.5226 -0.6139 -0.6902 -0.7494 -0.7905 -0.8128 -0.8168 -0.8039

-0.5397 -0.6351 -0.7137 -0.7736 -0.8131 -0.8320 -0.8311 -0.8115

-0.5443 -0.6403 -0.7191 -0.7778 -0.8155 -0.8318 -0.8273 -0.8036

-0.5358 -0.6290 -0.7049 -0.7614 -0.7969 -0.8112 -0.8049 -0.7793

-0.5143 -0.6011 -0.6718 -0.7243 -0.7573 -0.7703 -0.7637 -0.7388

-0.4814 -0.5580 -0.6211 -0.6683 -0.6982 -0.7104 -0.7048 -0.6822

-0.4379 -0.5025 -0.5553 -0.5958 -0.6220 -0.6333 -0.6296 -0.6110

-0.3835 -0.4366 -0.4784 -0.5101 -0.5319 -0.5423 -0.5405 -0.5267

-0.3190 -0.3607 -0.3928 -0.4160 -0.4317 -0.4403 -0.4406 -0.4315

-0.2459 -0.2767 -0.2999 -0.3161 -0.3262 -0.3317 -0.3329 -0.3282

-0.1666 -0.1868 -0.2018 -0.2121 -0.2181 -0.2208 -0.2212 -0.2194

-0.0836 -0.0936 -0.1010 -0.1059 -0.1088 -0.1099 -0.1097 -0.1089

0 0 0 0 0 0 0 0