pde3b.m running xmin=-1, xmax=1.2, nx=11, hx=0.22 ymin=-1, ymax=1, ny=11, hy=0.2 zmin=-1, zmax=1, nz=9, hz=0.25 initial conditions set iter= 0, diff=491.2713, error=3140.7495, avg= 5.5392, max= 12.2501 iter= 1, diff=347.1617, error=2805.3903, avg= 4.9478, max= 11.0724 iter= 2, diff=271.4204, error=2542.9856, avg= 4.4850, max= 9.4842 iter= 3, diff=222.1073, error=2326.1350, avg= 4.1025, max= 8.7979 iter= 4, diff=188.0796, error=2140.6525, avg= 3.7754, max= 8.3965 iter= 5, diff=162.9086, error=1978.8440, avg= 3.4900, max= 7.9507 iter= 6, diff=143.5431, error=1835.7022, avg= 3.2376, max= 7.5464 iter= 7, diff=128.0996, error=1707.7041, avg= 3.0118, max= 7.2045 iter= 8, diff=115.4479, error=1592.2646, avg= 2.8082, max= 6.8490 iter= 9, diff=104.8364, error=1487.4282, avg= 2.6233, max= 6.4897 iter= 10, diff= 95.7524, error=1391.6758, avg= 2.4545, max= 6.1988 iter= 11, diff= 87.8733, error=1303.8024, avg= 2.2995, max= 5.9211 iter= 12, diff= 80.9675, error=1222.8349, avg= 2.1567, max= 5.6395 iter= 13, diff= 74.8594, error=1147.9756, avg= 2.0246, max= 5.3579 iter= 14, diff= 69.4142, error=1078.5614, avg= 1.9022, max= 5.0811 iter= 15, diff= 64.5259, error=1014.0355, avg= 1.7884, max= 4.8152 iter= 16, diff= 60.1108, error= 953.9247, avg= 1.6824, max= 4.5671 iter= 17, diff= 56.1012, error= 897.8235, avg= 1.5835, max= 4.3269 iter= 18, diff= 52.4423, error= 845.3813, avg= 1.4910, max= 4.0948 iter= 19, diff= 49.0892, error= 796.2921, avg= 1.4044, max= 3.8724 iter= 20, diff= 46.0047, error= 750.2874, avg= 1.3233, max= 3.6592 iter= 21, diff= 43.1578, error= 707.1296, avg= 1.2471, max= 3.4562 iter= 22, diff= 40.5226, error= 666.6070, avg= 1.1757, max= 3.2627 iter= 23, diff= 38.0769, error= 628.5301, avg= 1.1085, max= 3.0793 iter= 24, diff= 35.8021, error= 592.7280, avg= 1.0454, max= 2.9050 iter= 25, diff= 33.6819, error= 559.0461, avg= 0.9860, max= 2.7403 iter= 26, diff= 31.7025, error= 527.3436, avg= 0.9301, max= 2.5842 iter= 27, diff= 29.8518, error= 497.4918, avg= 0.8774, max= 2.4404 iter= 28, diff= 28.1191, error= 469.3727, avg= 0.8278, max= 2.3081 iter= 29, diff= 26.4950, error= 442.8777, avg= 0.7811, max= 2.1822 iter= 30, diff= 24.9713, error= 417.9064, avg= 0.7370, max= 2.0629 iter= 31, diff= 23.5405, error= 394.3659, avg= 0.6955, max= 1.9495 iter= 32, diff= 22.1960, error= 372.1699, avg= 0.6564, max= 1.8423 iter= 33, diff= 20.9318, error= 351.2381, avg= 0.6195, max= 1.7405 iter= 34, diff= 19.7424, error= 331.4958, avg= 0.5846, max= 1.6443 iter= 35, diff= 18.6229, error= 312.8729, avg= 0.5518, max= 1.5532 iter= 36, diff= 17.5687, error= 295.3042, avg= 0.5208, max= 1.4671 iter= 37, diff= 16.5757, error= 278.7286, avg= 0.4916, max= 1.3855 iter= 38, diff= 15.6400, error= 263.0886, avg= 0.4640, max= 1.3085 iter= 39, diff= 14.7581, error= 248.3304, avg= 0.4380, max= 1.2356 iter= 40, diff= 13.9268, error= 234.4036, avg= 0.4134, max= 1.1668 iter= 41, diff= 13.1430, error= 221.2606, avg= 0.3902, max= 1.1017 iter= 42, diff= 12.4038, error= 208.8569, avg= 0.3684, max= 1.0403 iter= 43, diff= 11.7066, error= 197.1503, avg= 0.3477, max= 0.9822 iter= 44, diff= 11.0489, error= 186.1014, avg= 0.3282, max= 0.9274 iter= 45, diff= 10.4285, error= 175.6730, avg= 0.3098, max= 0.8755 iter= 46, diff= 9.8431, error= 165.8299, avg= 0.2925, max= 0.8267 iter= 47, diff= 9.2908, error= 156.5391, avg= 0.2761, max= 0.7804 iter= 48, diff= 8.7696, error= 147.7695, avg= 0.2606, max= 0.7368 iter= 49, diff= 8.2778, error= 139.4918, avg= 0.2460, max= 0.6956 computed solution u(x,y,2) plane -3.658 -1.486 0.360 1.928 3.268 4.429 5.458 6.403 7.311 -1.992 -0.142 1.438 2.798 3.989 5.061 6.062 7.037 8.032 -0.639 0.931 2.287 3.480 4.562 5.583 6.591 7.633 8.750 0.466 1.801 2.975 4.043 5.056 6.064 7.117 8.258 9.531 1.389 2.533 3.570 4.555 5.538 6.572 7.704 8.979 10.439 2.194 3.193 4.137 5.081 6.076 7.173 8.420 9.861 11.540 2.944 3.844 4.740 5.686 6.733 7.930 9.327 10.968 12.896 3.703 4.548 5.440 6.430 7.568 8.904 10.486 12.361 14.571 4.532 5.366 6.296 7.371 8.640 10.153 11.958 14.100 16.628 u(x,y,3) plane -2.407 -0.253 1.578 3.136 4.472 5.635 6.674 7.634 8.561 -1.034 0.781 2.332 3.672 4.856 5.933 6.951 7.955 8.987 0.029 1.551 2.866 4.032 5.104 6.132 7.164 8.245 9.414 0.850 2.127 3.254 4.289 5.289 6.306 7.387 8.576 9.909 1.494 2.577 3.564 4.515 5.485 6.527 7.689 9.014 10.539 2.026 2.967 3.864 4.775 5.757 6.862 8.138 9.627 11.367 2.511 3.360 4.216 5.134 6.170 7.374 8.796 10.477 12.459 3.009 3.818 4.680 5.650 6.780 8.121 9.721 11.625 13.875 3.583 4.398 5.312 6.376 7.641 9.157 10.970 13.129 15.677 u(x,y,4) plane -1.726 0.416 2.236 3.787 5.120 6.285 7.330 8.301 9.240 -0.530 1.261 2.792 4.120 5.298 6.378 7.408 8.431 9.488 0.358 1.846 3.135 4.283 5.347 6.380 7.429 8.536 9.740 1.007 2.245 3.340 4.355 5.346 6.368 7.468 8.688 10.063 1.483 2.525 3.479 4.407 5.368 6.416 7.599 8.957 10.524 1.853 2.754 3.619 4.509 5.482 6.592 7.888 9.409 11.190 2.178 2.994 3.822 4.722 5.750 6.959 8.397 10.107 12.123 2.522 3.306 4.148 5.104 6.229 7.573 9.186 11.110 13.385 2.943 3.745 4.648 5.705 6.968 8.485 10.305 12.474 15.036 u(x,y,5) plane -1.520 0.617 2.434 3.983 5.315 6.480 7.527 8.501 9.446 -0.384 1.399 2.923 4.246 5.423 6.504 7.538 8.568 9.634 0.446 1.923 3.202 4.344 5.405 6.439 7.494 8.611 9.827 1.037 2.262 3.346 4.353 5.341 6.365 7.472 8.703 10.092 1.458 2.485 3.427 4.347 5.305 6.355 7.545 8.915 10.498 1.773 2.660 3.514 4.396 5.366 6.479 7.781 9.313 11.109 2.046 2.850 3.668 4.562 5.587 6.798 8.242 9.961 11.990 2.338 3.113 3.948 4.900 6.022 7.368 8.985 10.916 13.201 2.709 3.506 4.405 5.460 6.721 8.239 10.062 12.235 14.801 u(x,y,6) plane -1.695 0.447 2.267 3.818 5.151 6.316 7.361 8.332 9.271 -0.499 1.292 2.823 4.150 5.329 6.409 7.438 8.462 9.519 0.389 1.877 3.166 4.314 5.378 6.410 7.459 8.567 9.771 1.038 2.275 3.371 4.385 5.376 6.398 7.499 8.719 10.094 1.514 2.555 3.509 4.437 5.398 6.446 7.629 8.987 10.555 1.884 2.784 3.649 4.539 5.512 6.623 7.918 9.439 11.221 2.209 3.025 3.853 4.752 5.780 6.990 8.428 10.137 12.154 2.553 3.337 4.179 5.135 6.259 7.604 9.217 11.141 13.416 2.974 3.776 4.679 5.736 6.998 8.516 10.336 12.505 15.067 u(x,y,7) plane -2.157 -0.003 1.827 3.385 4.721 5.885 6.923 7.884 8.810 -0.784 1.030 2.581 3.921 5.105 6.182 7.200 8.204 9.237 0.279 1.800 3.115 4.281 5.352 6.380 7.413 8.494 9.664 1.099 2.376 3.502 4.538 5.538 6.554 7.636 8.825 10.159 1.743 2.825 3.812 4.763 5.733 6.776 7.938 9.263 10.788 2.276 3.216 4.112 5.024 6.006 7.111 8.387 9.876 11.617 2.760 3.610 4.465 5.383 6.418 7.623 9.044 10.726 12.708 3.259 4.068 4.929 5.899 7.029 8.370 9.971 11.875 14.125 3.833 4.647 5.561 6.625 7.890 9.406 11.220 13.379 15.927 u(x,y,8) plane -2.815 -0.642 1.203 2.771 4.112 5.272 6.302 7.247 8.154 -1.149 0.701 2.281 3.641 4.832 5.904 6.905 7.880 8.875 0.204 1.774 3.129 4.322 5.404 6.426 7.434 8.476 9.593 1.310 2.644 3.818 4.885 5.898 6.907 7.959 9.101 10.374 2.232 3.376 4.413 5.397 6.381 7.415 8.547 9.822 11.282 3.037 4.036 4.980 5.924 6.919 8.016 9.263 10.704 12.383 3.787 4.687 5.583 6.529 7.575 8.773 10.170 11.811 13.740 4.546 5.391 6.283 7.273 8.411 9.747 11.329 13.204 15.415 5.376 6.210 7.139 8.214 9.484 10.997 12.801 14.944 17.471 difference exact-computed solution u(x,y,2) plane 0.0239 0.0457 0.0635 0.0755 0.0804 0.0774 0.0666 0.0488 0.0258 0.0456 0.0873 0.1212 0.1441 0.1534 0.1477 0.1270 0.0931 0.0492 0.0631 0.1207 0.1676 0.1993 0.2121 0.2042 0.1757 0.1287 0.0681 0.0746 0.1428 0.1982 0.2357 0.2509 0.2416 0.2077 0.1522 0.0805 0.0790 0.1512 0.2099 0.2496 0.2657 0.2557 0.2199 0.1612 0.0852 0.0757 0.1448 0.2011 0.2391 0.2544 0.2450 0.2106 0.1544 0.0816 0.0648 0.1240 0.1722 0.2047 0.2179 0.2097 0.1804 0.1321 0.0699 0.0474 0.0906 0.1258 0.1496 0.1591 0.1532 0.1317 0.0965 0.0510 0.0250 0.0478 0.0664 0.0789 0.0840 0.0808 0.0695 0.0509 0.0269 u(x,y,3) plane 0.0442 0.0845 0.1174 0.1396 0.1486 0.1431 0.1231 0.0902 0.0477 0.0843 0.1613 0.2240 0.2663 0.2836 0.2730 0.2348 0.1721 0.0910 0.1166 0.2231 0.3098 0.3684 0.3921 0.3776 0.3247 0.2380 0.1258 0.1379 0.2639 0.3665 0.4357 0.4638 0.4465 0.3840 0.2814 0.1488 0.1461 0.2795 0.3881 0.4613 0.4910 0.4728 0.4065 0.2979 0.1575 0.1400 0.2677 0.3718 0.4419 0.4704 0.4528 0.3894 0.2853 0.1508 0.1199 0.2293 0.3184 0.3785 0.4028 0.3877 0.3334 0.2443 0.1291 0.0876 0.1675 0.2326 0.2764 0.2942 0.2832 0.2435 0.1784 0.0943 0.0462 0.0884 0.1227 0.1459 0.1552 0.1494 0.1284 0.0941 0.0497 u(x,y,4) plane 0.0578 0.1105 0.1535 0.1825 0.1943 0.1871 0.1610 0.1180 0.0624 0.1102 0.2109 0.2929 0.3483 0.3708 0.3570 0.3070 0.2250 0.1190 0.1525 0.2917 0.4051 0.4816 0.5127 0.4936 0.4246 0.3111 0.1645 0.1804 0.3451 0.4792 0.5697 0.6064 0.5838 0.5021 0.3680 0.1945 0.1910 0.3654 0.5074 0.6032 0.6421 0.6181 0.5316 0.3895 0.2059 0.1830 0.3501 0.4861 0.5778 0.6150 0.5920 0.5091 0.3730 0.1972 0.1567 0.2998 0.4163 0.4948 0.5266 0.5069 0.4359 0.3194 0.1688 0.1145 0.2190 0.3041 0.3614 0.3846 0.3703 0.3183 0.2333 0.1233 0.0604 0.1155 0.1604 0.1907 0.2029 0.1953 0.1679 0.1230 0.0650 u(x,y,5) plane 0.0626 0.1198 0.1663 0.1978 0.2106 0.2027 0.1744 0.1278 0.0676 0.1194 0.2285 0.3174 0.3773 0.4017 0.3868 0.3327 0.2438 0.1289 0.1652 0.3160 0.4389 0.5218 0.5555 0.5348 0.4600 0.3371 0.1782 0.1954 0.3738 0.5192 0.6172 0.6570 0.6325 0.5440 0.3986 0.2107 0.2069 0.3959 0.5497 0.6535 0.6956 0.6697 0.5758 0.4220 0.2231 0.1983 0.3793 0.5267 0.6260 0.6663 0.6413 0.5515 0.4041 0.2136 0.1698 0.3248 0.4510 0.5361 0.5705 0.5492 0.4722 0.3460 0.1829 0.1240 0.2373 0.3295 0.3916 0.4167 0.4011 0.3449 0.2527 0.1336 0.0654 0.1252 0.1738 0.2066 0.2198 0.2116 0.1819 0.1333 0.0705 u(x,y,6) plane 0.0579 0.1108 0.1538 0.1829 0.1947 0.1875 0.1613 0.1182 0.0625 0.1105 0.2113 0.2935 0.3490 0.3715 0.3577 0.3076 0.2255 0.1192 0.1528 0.2923 0.4059 0.4826 0.5138 0.4946 0.4254 0.3117 0.1648 0.1807 0.3458 0.4802 0.5708 0.6076 0.5850 0.5031 0.3687 0.1949 0.1914 0.3661 0.5085 0.6044 0.6433 0.6193 0.5326 0.3902 0.2063 0.1834 0.3508 0.4871 0.5790 0.6162 0.5932 0.5100 0.3738 0.1976 0.1570 0.3004 0.4171 0.4958 0.5277 0.5079 0.4367 0.3200 0.1691 0.1147 0.2195 0.3047 0.3622 0.3854 0.3710 0.3189 0.2337 0.1235 0.0605 0.1158 0.1608 0.1911 0.2033 0.1957 0.1683 0.1233 0.0652 u(x,y,7) plane 0.0444 0.0849 0.1179 0.1401 0.1492 0.1437 0.1236 0.0906 0.0479 0.0846 0.1619 0.2249 0.2674 0.2846 0.2740 0.2357 0.1727 0.0913 0.1170 0.2239 0.3110 0.3697 0.3936 0.3790 0.3259 0.2388 0.1263 0.1385 0.2649 0.3679 0.4373 0.4655 0.4481 0.3854 0.2824 0.1493 0.1466 0.2805 0.3895 0.4631 0.4928 0.4745 0.4080 0.2990 0.1580 0.1405 0.2687 0.3732 0.4435 0.4721 0.4544 0.3908 0.2863 0.1514 0.1203 0.2302 0.3196 0.3798 0.4042 0.3891 0.3345 0.2451 0.1296 0.0879 0.1681 0.2334 0.2774 0.2953 0.2842 0.2444 0.1790 0.0946 0.0464 0.0887 0.1232 0.1464 0.1558 0.1499 0.1289 0.0944 0.0499 u(x,y,8) plane 0.0240 0.0460 0.0638 0.0759 0.0808 0.0778 0.0669 0.0490 0.0259 0.0458 0.0877 0.1218 0.1448 0.1541 0.1484 0.1276 0.0936 0.0495 0.0634 0.1213 0.1684 0.2002 0.2132 0.2052 0.1765 0.1293 0.0684 0.0750 0.1435 0.1992 0.2368 0.2521 0.2427 0.2087 0.1530 0.0809 0.0794 0.1519 0.2110 0.2508 0.2669 0.2569 0.2210 0.1619 0.0856 0.0761 0.1455 0.2021 0.2402 0.2557 0.2461 0.2116 0.1551 0.0820 0.0652 0.1246 0.1731 0.2057 0.2189 0.2107 0.1812 0.1327 0.0702 0.0476 0.0911 0.1264 0.1503 0.1599 0.1539 0.1323 0.0970 0.0512 0.0251 0.0480 0.0667 0.0793 0.0844 0.0812 0.0698 0.0511 0.0270 iter= 50, diff= 7.8136, error= 131.6782, avg= 0.2322, max= 0.6567 iter= 51, diff= 7.3756, error= 124.3026, avg= 0.2192, max= 0.6199 iter= 52, diff= 6.9622, error= 117.3404, avg= 0.2069, max= 0.5853 iter= 53, diff= 6.5720, error= 110.7684, avg= 0.1954, max= 0.5525 iter= 54, diff= 6.2037, error= 104.5647, avg= 0.1844, max= 0.5216 iter= 55, diff= 5.8561, error= 98.7085, avg= 0.1741, max= 0.4924 iter= 56, diff= 5.5280, error= 93.1805, avg= 0.1643, max= 0.4649 iter= 57, diff= 5.2183, error= 87.9622, avg= 0.1551, max= 0.4388 iter= 58, diff= 4.9260, error= 83.0362, avg= 0.1464, max= 0.4143 iter= 59, diff= 4.6501, error= 78.3861, avg= 0.1382, max= 0.3911 iter= 60, diff= 4.3896, error= 73.9965, avg= 0.1305, max= 0.3692 iter= 61, diff= 4.1438, error= 69.8527, avg= 0.1232, max= 0.3485 iter= 62, diff= 3.9117, error= 65.9411, avg= 0.1163, max= 0.3290 iter= 63, diff= 3.6926, error= 62.2485, avg= 0.1098, max= 0.3106 iter= 64, diff= 3.4858, error= 58.7627, avg= 0.1036, max= 0.2932 iter= 65, diff= 3.2906, error= 55.4721, avg= 0.0978, max= 0.2768 iter= 66, diff= 3.1063, error= 52.3658, avg= 0.0924, max= 0.2613 iter= 67, diff= 2.9323, error= 49.4335, avg= 0.0872, max= 0.2466 iter= 68, diff= 2.7681, error= 46.6654, avg= 0.0823, max= 0.2328 iter= 69, diff= 2.6131, error= 44.0523, avg= 0.0777, max= 0.2198 iter= 70, diff= 2.4668, error= 41.5855, avg= 0.0733, max= 0.2075 iter= 71, diff= 2.3286, error= 39.2569, avg= 0.0692, max= 0.1959 iter= 72, diff= 2.1982, error= 37.0586, avg= 0.0654, max= 0.1849 iter= 73, diff= 2.0751, error= 34.9835, avg= 0.0617, max= 0.1746 iter= 74, diff= 1.9589, error= 33.0245, avg= 0.0582, max= 0.1648 iter= 75, diff= 1.8492, error= 31.1753, avg= 0.0550, max= 0.1556 iter= 76, diff= 1.7457, error= 29.4296, avg= 0.0519, max= 0.1469 iter= 77, diff= 1.6479, error= 27.7817, avg= 0.0490, max= 0.1386 iter= 78, diff= 1.5557, error= 26.2260, avg= 0.0463, max= 0.1309 iter= 79, diff= 1.4685, error= 24.7575, avg= 0.0437, max= 0.1235 iter= 80, diff= 1.3863, error= 23.3712, avg= 0.0412, max= 0.1166 iter= 81, diff= 1.3087, error= 22.0625, avg= 0.0389, max= 0.1101 iter= 82, diff= 1.2354, error= 20.8271, avg= 0.0367, max= 0.1039 iter= 83, diff= 1.1662, error= 19.6609, avg= 0.0347, max= 0.0981 iter= 84, diff= 1.1009, error= 18.5599, avg= 0.0327, max= 0.0926 iter= 85, diff= 1.0393, error= 17.5207, avg= 0.0309, max= 0.0874 iter= 86, diff= 0.9811, error= 16.5396, avg= 0.0292, max= 0.0825 iter= 87, diff= 0.9261, error= 15.6134, avg= 0.0275, max= 0.0779 iter= 88, diff= 0.8743, error= 14.7392, avg= 0.0260, max= 0.0735 iter= 89, diff= 0.8253, error= 13.9138, avg= 0.0245, max= 0.0694 iter= 90, diff= 0.7791, error= 13.1347, avg= 0.0232, max= 0.0655 iter= 91, diff= 0.7355, error= 12.3992, avg= 0.0219, max= 0.0619 iter= 92, diff= 0.6943, error= 11.7049, avg= 0.0206, max= 0.0584 iter= 93, diff= 0.6554, error= 11.0495, avg= 0.0195, max= 0.0551 iter= 94, diff= 0.6187, error= 10.4308, avg= 0.0184, max= 0.0520 iter= 95, diff= 0.5841, error= 9.8467, avg= 0.0174, max= 0.0491 iter= 96, diff= 0.5514, error= 9.2953, avg= 0.0164, max= 0.0464 iter= 97, diff= 0.5205, error= 8.7748, avg= 0.0155, max= 0.0438 iter= 98, diff= 0.4914, error= 8.2835, avg= 0.0146, max= 0.0413 iter= 99, diff= 0.4638, error= 7.8197, avg= 0.0138, max= 0.0390 computed solution u(x,y,2) plane -3.636 -1.443 0.420 1.999 3.344 4.502 5.521 6.450 7.335 -1.949 -0.060 1.552 2.934 4.134 5.200 6.181 7.125 8.078 -0.580 1.045 2.444 3.667 4.762 5.776 6.757 7.754 8.814 0.537 1.935 3.162 4.265 5.292 6.292 7.313 8.402 9.607 1.464 2.675 3.768 4.790 5.789 6.814 7.912 9.131 10.520 2.265 3.329 4.327 5.307 6.317 7.405 8.619 10.007 11.617 3.005 3.961 4.903 5.879 6.938 8.129 9.497 11.093 12.962 3.747 4.634 5.559 6.571 7.718 9.049 10.611 12.452 14.620 4.556 5.412 6.359 7.445 8.720 10.230 12.023 14.148 16.653 u(x,y,3) plane -2.365 -0.173 1.688 3.267 4.612 5.770 6.790 7.719 8.606 -0.955 0.933 2.543 3.923 5.123 6.190 7.172 8.117 9.073 0.139 1.761 3.158 4.379 5.473 6.488 7.471 8.470 9.533 0.980 2.375 3.599 4.700 5.727 6.728 7.750 8.842 10.050 1.631 2.840 3.930 4.950 5.948 6.974 8.074 9.296 10.687 2.158 3.219 4.214 5.192 6.202 7.290 8.506 9.897 11.510 2.624 3.577 4.516 5.491 6.550 7.741 9.111 10.708 12.581 3.092 3.976 4.900 5.911 7.058 8.389 9.952 11.794 13.964 3.627 4.481 5.427 6.514 7.788 9.298 11.092 13.218 15.724 u(x,y,4) plane -1.672 0.520 2.381 3.959 5.304 6.462 7.482 8.412 9.299 -0.427 1.459 3.068 4.448 5.648 6.715 7.698 8.644 9.601 0.501 2.121 3.517 4.737 5.831 6.846 7.830 8.830 9.895 1.177 2.570 3.792 4.892 5.918 6.919 7.943 9.036 10.247 1.663 2.869 3.957 4.976 5.974 7.000 8.101 9.325 10.719 2.025 3.084 4.077 5.054 6.063 7.152 8.369 9.761 11.377 2.326 3.277 4.215 5.189 6.248 7.439 8.810 10.409 12.283 2.630 3.513 4.435 5.445 6.592 7.923 9.487 11.331 13.502 3.000 3.854 4.800 5.885 7.159 8.670 10.464 12.591 15.097 u(x,y,5) plane -1.461 0.730 2.591 4.169 5.513 6.672 7.692 8.622 9.510 -0.272 1.614 3.222 4.602 5.801 6.869 7.852 8.798 9.756 0.601 2.220 3.616 4.836 5.929 6.944 7.928 8.930 9.995 1.221 2.614 3.835 4.935 5.961 6.962 7.986 9.080 10.291 1.653 2.858 3.945 4.964 5.962 6.988 8.089 9.314 10.709 1.960 3.018 4.010 4.987 5.996 7.085 8.302 9.695 11.312 2.206 3.156 4.094 5.068 6.126 7.317 8.688 10.288 12.163 2.455 3.337 4.259 5.269 6.416 7.747 9.311 11.155 13.327 2.770 3.624 4.570 5.655 6.929 8.439 10.234 12.361 14.868 u(x,y,6) plane -1.640 0.551 2.412 3.991 5.335 6.493 7.513 8.443 9.330 -0.395 1.490 3.099 4.479 5.679 6.746 7.729 8.675 9.632 0.533 2.152 3.548 4.769 5.862 6.877 7.861 8.862 9.926 1.208 2.601 3.823 4.923 5.950 6.951 7.974 9.067 10.278 1.695 2.900 3.988 5.007 6.006 7.031 8.132 9.356 10.750 2.056 3.115 4.108 5.085 6.094 7.183 8.400 9.793 11.408 2.357 3.308 4.246 5.220 6.279 7.470 8.841 10.440 12.314 2.661 3.544 4.466 5.477 6.623 7.955 9.518 11.362 13.533 3.031 3.885 4.831 5.917 7.191 8.701 10.496 12.622 15.129 u(x,y,7) plane -2.115 0.077 1.938 3.517 4.862 6.020 7.040 7.969 8.856 -0.705 1.183 2.793 4.173 5.373 6.440 7.422 8.367 9.323 0.389 2.011 3.408 4.629 5.723 6.738 7.721 8.720 9.783 1.230 2.625 3.849 4.950 5.977 6.978 8.000 9.092 10.300 1.881 3.090 4.180 5.200 6.198 7.224 8.324 9.546 10.937 2.408 3.469 4.464 5.442 6.452 7.540 8.756 10.147 11.760 2.874 3.827 4.766 5.741 6.800 7.991 9.361 10.958 12.831 3.342 4.226 5.150 6.161 7.308 8.639 10.202 12.044 14.214 3.877 4.731 5.677 6.764 8.038 9.548 11.342 13.468 15.974 u(x,y,8) plane -2.792 -0.599 1.263 2.843 4.188 5.346 6.365 7.293 8.179 -1.105 0.784 2.395 3.777 4.977 6.044 7.025 7.969 8.922 0.264 1.889 3.288 4.511 5.606 6.620 7.601 8.598 9.658 1.380 2.779 4.006 5.108 6.136 7.136 8.157 9.245 10.450 2.307 3.519 4.612 5.634 6.633 7.658 8.756 9.975 11.363 3.109 4.173 5.171 6.151 7.160 8.248 9.463 10.851 12.460 3.849 4.805 5.746 6.723 7.782 8.972 10.341 11.936 13.806 4.591 5.477 6.402 7.415 8.562 9.893 11.455 13.296 15.463 5.400 6.255 7.202 8.289 9.563 11.073 12.867 14.992 17.497 difference exact-computed solution u(x,y,2) plane 0.0014 0.0027 0.0037 0.0044 0.0046 0.0044 0.0037 0.0027 0.0014 0.0027 0.0051 0.0071 0.0083 0.0088 0.0083 0.0071 0.0052 0.0027 0.0037 0.0071 0.0098 0.0115 0.0121 0.0115 0.0098 0.0071 0.0037 0.0044 0.0083 0.0115 0.0135 0.0142 0.0135 0.0115 0.0084 0.0044 0.0046 0.0088 0.0121 0.0142 0.0149 0.0142 0.0121 0.0088 0.0046 0.0044 0.0083 0.0115 0.0135 0.0142 0.0135 0.0115 0.0084 0.0044 0.0037 0.0071 0.0098 0.0115 0.0121 0.0115 0.0098 0.0071 0.0037 0.0027 0.0052 0.0071 0.0084 0.0088 0.0084 0.0071 0.0052 0.0027 0.0014 0.0027 0.0037 0.0044 0.0046 0.0044 0.0037 0.0027 0.0014 u(x,y,3) plane 0.0026 0.0050 0.0069 0.0081 0.0085 0.0081 0.0069 0.0050 0.0026 0.0050 0.0095 0.0131 0.0154 0.0162 0.0154 0.0131 0.0095 0.0050 0.0069 0.0131 0.0180 0.0212 0.0223 0.0212 0.0181 0.0131 0.0069 0.0081 0.0154 0.0212 0.0249 0.0262 0.0250 0.0212 0.0154 0.0081 0.0085 0.0162 0.0223 0.0262 0.0276 0.0263 0.0223 0.0162 0.0085 0.0081 0.0154 0.0212 0.0250 0.0263 0.0250 0.0213 0.0155 0.0081 0.0069 0.0131 0.0181 0.0212 0.0223 0.0213 0.0181 0.0132 0.0069 0.0050 0.0095 0.0131 0.0154 0.0162 0.0155 0.0132 0.0096 0.0050 0.0026 0.0050 0.0069 0.0081 0.0085 0.0081 0.0069 0.0050 0.0026 u(x,y,4) plane 0.0034 0.0065 0.0090 0.0106 0.0111 0.0106 0.0090 0.0065 0.0034 0.0065 0.0124 0.0171 0.0201 0.0212 0.0201 0.0171 0.0125 0.0065 0.0090 0.0171 0.0235 0.0277 0.0291 0.0277 0.0236 0.0171 0.0090 0.0106 0.0201 0.0277 0.0326 0.0343 0.0326 0.0277 0.0202 0.0106 0.0111 0.0212 0.0291 0.0343 0.0360 0.0343 0.0292 0.0212 0.0112 0.0106 0.0201 0.0277 0.0326 0.0343 0.0326 0.0278 0.0202 0.0106 0.0090 0.0171 0.0236 0.0277 0.0292 0.0278 0.0236 0.0172 0.0090 0.0065 0.0125 0.0171 0.0202 0.0212 0.0202 0.0172 0.0125 0.0066 0.0034 0.0065 0.0090 0.0106 0.0112 0.0106 0.0090 0.0066 0.0035 u(x,y,5) plane 0.0037 0.0071 0.0097 0.0114 0.0120 0.0115 0.0097 0.0071 0.0037 0.0071 0.0134 0.0185 0.0218 0.0229 0.0218 0.0185 0.0135 0.0071 0.0097 0.0185 0.0255 0.0300 0.0315 0.0300 0.0255 0.0186 0.0098 0.0114 0.0218 0.0300 0.0353 0.0371 0.0353 0.0300 0.0218 0.0115 0.0120 0.0229 0.0315 0.0371 0.0390 0.0371 0.0316 0.0230 0.0121 0.0115 0.0218 0.0300 0.0353 0.0371 0.0353 0.0301 0.0219 0.0115 0.0097 0.0185 0.0255 0.0300 0.0316 0.0301 0.0256 0.0186 0.0098 0.0071 0.0135 0.0186 0.0218 0.0230 0.0219 0.0186 0.0135 0.0071 0.0037 0.0071 0.0098 0.0115 0.0121 0.0115 0.0098 0.0071 0.0037 u(x,y,6) plane 0.0034 0.0065 0.0090 0.0106 0.0111 0.0106 0.0090 0.0065 0.0034 0.0065 0.0124 0.0171 0.0201 0.0212 0.0201 0.0171 0.0125 0.0065 0.0090 0.0171 0.0235 0.0277 0.0291 0.0277 0.0236 0.0171 0.0090 0.0106 0.0201 0.0277 0.0326 0.0343 0.0326 0.0278 0.0202 0.0106 0.0111 0.0212 0.0291 0.0343 0.0361 0.0343 0.0292 0.0212 0.0112 0.0106 0.0201 0.0277 0.0326 0.0343 0.0326 0.0278 0.0202 0.0106 0.0090 0.0171 0.0236 0.0278 0.0292 0.0278 0.0236 0.0172 0.0090 0.0065 0.0125 0.0171 0.0202 0.0212 0.0202 0.0172 0.0125 0.0066 0.0034 0.0065 0.0090 0.0106 0.0112 0.0106 0.0090 0.0066 0.0035 u(x,y,7) plane 0.0026 0.0050 0.0069 0.0081 0.0085 0.0081 0.0069 0.0050 0.0026 0.0050 0.0095 0.0131 0.0154 0.0162 0.0154 0.0131 0.0095 0.0050 0.0069 0.0131 0.0180 0.0212 0.0223 0.0212 0.0181 0.0131 0.0069 0.0081 0.0154 0.0212 0.0249 0.0262 0.0250 0.0212 0.0154 0.0081 0.0085 0.0162 0.0223 0.0262 0.0276 0.0263 0.0223 0.0162 0.0085 0.0081 0.0154 0.0212 0.0250 0.0263 0.0250 0.0213 0.0155 0.0081 0.0069 0.0131 0.0181 0.0212 0.0223 0.0213 0.0181 0.0132 0.0069 0.0050 0.0095 0.0131 0.0154 0.0162 0.0155 0.0132 0.0096 0.0050 0.0026 0.0050 0.0069 0.0081 0.0085 0.0081 0.0069 0.0050 0.0026 u(x,y,8) plane 0.0014 0.0027 0.0037 0.0044 0.0046 0.0044 0.0037 0.0027 0.0014 0.0027 0.0051 0.0071 0.0083 0.0088 0.0083 0.0071 0.0052 0.0027 0.0037 0.0071 0.0098 0.0115 0.0121 0.0115 0.0098 0.0071 0.0037 0.0044 0.0083 0.0115 0.0135 0.0142 0.0135 0.0115 0.0084 0.0044 0.0046 0.0088 0.0121 0.0142 0.0149 0.0142 0.0121 0.0088 0.0046 0.0044 0.0083 0.0115 0.0135 0.0142 0.0135 0.0115 0.0084 0.0044 0.0037 0.0071 0.0098 0.0115 0.0121 0.0115 0.0098 0.0071 0.0037 0.0027 0.0052 0.0071 0.0084 0.0088 0.0084 0.0071 0.0052 0.0027 0.0014 0.0027 0.0037 0.0044 0.0046 0.0044 0.0037 0.0027 0.0014 iter= 100, diff= 0.4379, error= 7.3818, avg= 0.0130, max= 0.0368 iter= 101, diff= 0.4133, error= 6.9684, avg= 0.0123, max= 0.0348 iter= 102, diff= 0.3902, error= 6.5782, avg= 0.0116, max= 0.0328 iter= 103, diff= 0.3684, error= 6.2099, avg= 0.0110, max= 0.0310 iter= 104, diff= 0.3477, error= 5.8622, avg= 0.0103, max= 0.0293 iter= 105, diff= 0.3283, error= 5.5339, avg= 0.0098, max= 0.0276 iter= 106, diff= 0.3099, error= 5.2240, avg= 0.0092, max= 0.0261 iter= 107, diff= 0.2925, error= 4.9315, avg= 0.0087, max= 0.0246 iter= 108, diff= 0.2761, error= 4.6554, avg= 0.0082, max= 0.0232 iter= 109, diff= 0.2607, error= 4.3947, avg= 0.0078, max= 0.0219 iter= 110, diff= 0.2461, error= 4.1486, avg= 0.0073, max= 0.0207 iter= 111, diff= 0.2323, error= 3.9163, avg= 0.0069, max= 0.0195 iter= 112, diff= 0.2193, error= 3.6970, avg= 0.0065, max= 0.0184 iter= 113, diff= 0.2070, error= 3.4900, avg= 0.0062, max= 0.0174 iter= 114, diff= 0.1954, error= 3.2946, avg= 0.0058, max= 0.0164 iter= 115, diff= 0.1845, error= 3.1101, avg= 0.0055, max= 0.0155 iter= 116, diff= 0.1742, error= 2.9359, avg= 0.0052, max= 0.0147 iter= 117, diff= 0.1644, error= 2.7715, avg= 0.0049, max= 0.0138 iter= 118, diff= 0.1552, error= 2.6163, avg= 0.0046, max= 0.0131 iter= 119, diff= 0.1465, error= 2.4698, avg= 0.0044, max= 0.0123 iter= 120, diff= 0.1383, error= 2.3315, avg= 0.0041, max= 0.0116 iter= 121, diff= 0.1306, error= 2.2010, avg= 0.0039, max= 0.0110 iter= 122, diff= 0.1232, error= 2.0777, avg= 0.0037, max= 0.0104 iter= 123, diff= 0.1163, error= 1.9614, avg= 0.0035, max= 0.0098 iter= 124, diff= 0.1098, error= 1.8516, avg= 0.0033, max= 0.0092 iter= 125, diff= 0.1037, error= 1.7479, avg= 0.0031, max= 0.0087 iter= 126, diff= 0.0979, error= 1.6500, avg= 0.0029, max= 0.0082 iter= 127, diff= 0.0924, error= 1.5576, avg= 0.0027, max= 0.0078 iter= 128, diff= 0.0872, error= 1.4704, avg= 0.0026, max= 0.0073 iter= 129, diff= 0.0823, error= 1.3881, avg= 0.0024, max= 0.0069 iter= 130, diff= 0.0777, error= 1.3103, avg= 0.0023, max= 0.0065 iter= 131, diff= 0.0734, error= 1.2370, avg= 0.0022, max= 0.0062 iter= 132, diff= 0.0693, error= 1.1677, avg= 0.0021, max= 0.0058 iter= 133, diff= 0.0654, error= 1.1023, avg= 0.0019, max= 0.0055 iter= 134, diff= 0.0617, error= 1.0406, avg= 0.0018, max= 0.0052 iter= 135, diff= 0.0583, error= 0.9823, avg= 0.0017, max= 0.0049 iter= 136, diff= 0.0550, error= 0.9273, avg= 0.0016, max= 0.0046 iter= 137, diff= 0.0519, error= 0.8754, avg= 0.0015, max= 0.0044 iter= 138, diff= 0.0490, error= 0.8264, avg= 0.0015, max= 0.0041 iter= 139, diff= 0.0463, error= 0.7801, avg= 0.0014, max= 0.0039 iter= 140, diff= 0.0437, error= 0.7364, avg= 0.0013, max= 0.0037 iter= 141, diff= 0.0412, error= 0.6952, avg= 0.0012, max= 0.0035 iter= 142, diff= 0.0389, error= 0.6563, avg= 0.0012, max= 0.0033 iter= 143, diff= 0.0367, error= 0.6195, avg= 0.0011, max= 0.0031 iter= 144, diff= 0.0347, error= 0.5848, avg= 0.0010, max= 0.0029 iter= 145, diff= 0.0327, error= 0.5521, avg= 0.0010, max= 0.0028 iter= 146, diff= 0.0309, error= 0.5212, avg= 0.0009, max= 0.0026 iter= 147, diff= 0.0292, error= 0.4920, avg= 0.0009, max= 0.0025 iter= 148, diff= 0.0275, error= 0.4644, avg= 0.0008, max= 0.0023 exact solution u(x,y,1) plane -11.000 -8.032 -5.496 -3.344 -1.528 0.000 1.288 2.384 3.336 4.192 5.000 -8.151 -5.578 -3.383 -1.520 0.060 1.405 2.563 3.582 4.509 5.393 6.282 -5.723 -3.505 -1.613 0.001 1.384 2.584 3.651 4.630 5.572 6.523 7.532 -3.651 -1.749 -0.121 1.281 2.506 3.601 4.614 5.594 6.588 7.645 8.812 -1.871 -0.247 1.155 2.385 3.490 4.518 5.518 6.536 7.622 8.823 10.187 -0.319 1.065 2.281 3.377 4.401 5.401 6.425 7.521 8.737 10.121 11.721 1.068 2.251 3.319 4.320 5.302 6.313 7.400 8.612 9.997 11.603 13.478 2.354 3.376 4.335 5.279 6.258 7.317 8.507 9.874 11.467 13.333 15.521 3.604 4.502 5.391 6.318 7.331 8.479 9.809 11.370 13.209 15.374 17.914 4.880 5.694 6.551 7.499 8.587 9.861 11.371 13.164 15.288 17.791 20.722 6.248 7.016 7.880 8.888 10.088 11.528 13.256 15.320 17.768 20.648 24.008 u(x,y,2) plane -8.672 -5.704 -3.168 -1.016 0.800 2.328 3.616 4.712 5.664 6.520 7.328 -6.208 -3.634 -1.440 0.423 2.004 3.349 4.506 5.525 6.452 7.336 8.225 -4.165 -1.946 -0.055 1.559 2.942 4.143 5.209 6.189 7.130 8.081 9.090 -2.477 -0.576 1.052 2.454 3.679 4.774 5.787 6.767 7.761 8.818 9.985 -1.082 0.541 1.944 3.173 4.278 5.306 6.306 7.324 8.410 9.611 10.975 0.084 1.468 2.684 3.780 4.804 5.804 6.828 7.924 9.140 10.524 12.124 1.086 2.269 3.338 4.339 5.320 6.331 7.418 8.630 10.015 11.621 13.496 1.987 3.009 3.968 4.913 5.891 6.951 8.140 9.507 11.100 12.966 15.154 2.852 3.750 4.639 5.566 6.579 7.727 9.057 10.618 12.457 14.622 17.162 3.744 4.557 5.414 6.362 7.450 8.724 10.234 12.027 14.151 16.655 19.585 4.726 5.494 6.358 7.366 8.566 10.006 11.734 13.798 16.246 19.126 22.486 u(x,y,3) plane -7.125 -4.157 -1.621 0.531 2.347 3.875 5.163 6.259 7.211 8.067 8.875 -4.936 -2.363 -0.168 1.695 3.275 4.620 5.778 6.797 7.724 8.608 9.497 -3.168 -0.950 0.942 2.556 3.939 5.139 6.206 7.185 8.127 9.078 10.087 -1.756 0.146 1.774 3.176 4.401 5.496 6.509 7.489 8.483 9.540 10.707 -0.636 0.988 2.390 3.620 4.725 5.753 6.753 7.771 8.857 10.058 11.422 0.256 1.640 2.856 3.952 4.976 5.976 7.000 8.096 9.312 10.696 12.296 0.983 2.166 3.234 4.235 5.217 6.228 7.315 8.527 9.912 11.518 13.393 1.609 2.631 3.590 4.534 5.513 6.572 7.762 9.129 10.722 12.588 14.776 2.199 3.097 3.986 4.913 5.926 7.074 8.404 9.965 11.804 13.969 16.509 2.815 3.629 4.486 5.434 6.522 7.796 9.306 11.099 13.223 15.726 18.657 3.523 4.291 5.155 6.163 7.363 8.803 10.531 12.595 15.043 17.923 21.283 u(x,y,4) plane -6.266 -3.298 -0.762 1.390 3.206 4.734 6.022 7.118 8.070 8.926 9.734 -4.242 -1.668 0.526 2.390 3.970 5.315 6.473 7.491 8.419 9.303 10.192 -2.638 -0.420 1.472 3.085 4.468 5.669 6.735 7.715 8.656 9.607 10.616 -1.391 0.510 2.138 3.540 4.765 5.860 6.874 7.853 8.848 9.904 11.071 -0.436 1.187 2.590 3.820 4.924 5.953 6.952 7.971 9.056 10.257 11.621 0.290 1.674 2.890 3.986 5.010 6.010 7.034 8.130 9.346 10.730 12.330 0.852 2.036 3.104 4.105 5.087 6.097 7.185 8.397 9.782 11.387 13.262 1.314 2.335 3.294 4.239 5.217 6.277 7.466 8.833 10.426 12.292 14.480 1.738 2.636 3.525 4.452 5.466 6.613 7.944 9.504 11.343 13.509 16.049 2.190 3.004 3.860 4.809 5.896 7.171 8.680 10.473 12.597 15.101 18.031 2.732 3.500 4.364 5.372 6.572 8.012 9.740 11.804 14.252 17.132 20.492 u(x,y,5) plane -6.000 -3.032 -0.496 1.656 3.472 5.000 6.288 7.384 8.336 9.192 10.000 -4.031 -1.458 0.737 2.600 4.180 5.525 6.683 7.702 8.629 9.513 10.402 -2.483 -0.265 1.627 3.241 4.624 5.824 6.891 7.870 8.812 9.763 10.772 -1.291 0.611 2.239 3.641 4.866 5.961 6.974 7.954 8.948 10.005 11.172 -0.391 1.233 2.635 3.865 4.970 5.998 6.998 8.016 9.102 10.303 11.667 0.281 1.665 2.881 3.977 5.001 6.001 7.025 8.121 9.337 10.721 12.321 0.788 1.971 3.039 4.040 5.022 6.033 7.120 8.332 9.717 11.323 13.198 1.194 2.216 3.175 4.119 5.098 6.157 7.347 8.714 10.307 12.173 14.361 1.564 2.462 3.351 4.278 5.291 6.439 7.769 9.330 11.169 13.334 15.874 1.960 2.774 3.631 4.579 5.667 6.941 8.451 10.244 12.368 14.871 17.802 2.448 3.216 4.080 5.088 6.288 7.728 9.456 11.520 13.968 16.848 20.208 u(x,y,6) plane -6.234 -3.266 -0.730 1.422 3.238 4.766 6.054 7.150 8.102 8.958 9.766 -4.211 -1.637 0.558 2.421 4.001 5.346 6.504 7.522 8.450 9.334 10.223 -2.607 -0.389 1.503 3.116 4.499 5.700 6.766 7.746 8.688 9.639 10.647 -1.360 0.542 2.169 3.572 4.796 5.891 6.905 7.885 8.879 9.935 11.103 -0.405 1.218 2.621 3.851 4.956 5.984 6.983 8.002 9.088 10.289 11.653 0.322 1.706 2.922 4.018 5.042 6.042 7.066 8.162 9.378 10.762 12.362 0.884 2.067 3.135 4.136 5.118 6.128 7.216 8.428 9.813 11.419 13.293 1.345 2.366 3.325 4.270 5.248 6.308 7.498 8.865 10.457 12.323 14.511 1.769 2.668 3.556 4.483 5.497 6.645 7.975 9.535 11.375 13.540 16.080 2.221 3.035 3.892 4.840 5.927 7.202 8.712 10.505 12.629 15.132 18.063 2.764 3.532 4.396 5.404 6.604 8.044 9.772 11.836 14.284 17.164 20.524 u(x,y,7) plane -6.875 -3.907 -1.371 0.781 2.597 4.125 5.413 6.509 7.461 8.317 9.125 -4.686 -2.113 0.082 1.945 3.525 4.870 6.028 7.047 7.974 8.858 9.747 -2.918 -0.700 1.192 2.806 4.189 5.389 6.456 7.435 8.377 9.328 10.337 -1.506 0.396 2.024 3.426 4.651 5.746 6.759 7.739 8.733 9.790 10.957 -0.386 1.238 2.640 3.870 4.975 6.003 7.003 8.021 9.107 10.308 11.672 0.506 1.890 3.106 4.202 5.226 6.226 7.250 8.346 9.562 10.946 12.546 1.233 2.416 3.484 4.485 5.467 6.478 7.565 8.777 10.162 11.768 13.643 1.859 2.881 3.840 4.784 5.763 6.822 8.012 9.379 10.972 12.838 15.026 2.449 3.347 4.236 5.163 6.176 7.324 8.654 10.215 12.054 14.219 16.759 3.065 3.879 4.736 5.684 6.772 8.046 9.556 11.349 13.473 15.976 18.907 3.773 4.541 5.405 6.413 7.613 9.053 10.781 12.845 15.293 18.173 21.533 u(x,y,8) plane -7.828 -4.860 -2.324 -0.172 1.644 3.172 4.460 5.556 6.508 7.364 8.172 -5.364 -2.791 -0.596 1.267 2.847 4.192 5.350 6.369 7.296 8.180 9.069 -3.321 -1.103 0.789 2.403 3.786 4.986 6.052 7.032 7.974 8.925 9.933 -1.634 0.268 1.896 3.298 4.523 5.618 6.631 7.611 8.605 9.662 10.829 -0.239 1.385 2.787 4.017 5.122 6.150 7.150 8.168 9.254 10.455 11.819 0.928 2.312 3.528 4.624 5.648 6.648 7.672 8.768 9.984 11.368 12.968 1.930 3.113 4.181 5.182 6.164 7.175 8.262 9.474 10.859 12.465 14.339 2.831 3.853 4.812 5.756 6.734 7.794 8.984 10.351 11.943 13.810 15.998 3.696 4.594 5.483 6.410 7.423 8.571 9.901 11.462 13.301 15.466 18.006 4.587 5.401 6.258 7.206 8.294 9.568 11.078 12.871 14.995 17.498 20.429 5.570 6.338 7.202 8.210 9.410 10.850 12.578 14.642 17.090 19.970 23.330 u(x,y,9) plane -9.000 -6.032 -3.496 -1.344 0.472 2.000 3.288 4.384 5.336 6.192 7.000 -6.151 -3.578 -1.383 0.480 2.060 3.405 4.563 5.582 6.509 7.393 8.282 -3.723 -1.505 0.387 2.001 3.384 4.584 5.651 6.630 7.572 8.523 9.532 -1.651 0.251 1.879 3.281 4.506 5.601 6.614 7.594 8.588 9.645 10.812 0.129 1.753 3.155 4.385 5.490 6.518 7.518 8.536 9.622 10.823 12.187 1.681 3.065 4.281 5.377 6.401 7.401 8.425 9.521 10.737 12.121 13.721 3.068 4.251 5.319 6.320 7.302 8.313 9.400 10.612 11.997 13.603 15.478 4.354 5.376 6.335 7.279 8.258 9.317 10.507 11.874 13.467 15.333 17.521 5.604 6.502 7.391 8.318 9.331 10.479 11.809 13.370 15.209 17.374 19.914 6.880 7.694 8.551 9.499 10.587 11.861 13.371 15.164 17.288 19.791 22.722 8.248 9.016 9.880 10.888 12.088 13.528 15.256 17.320 19.768 22.648 26.008 computed solution u(x,y,2) plane -3.635 -1.440 0.423 2.003 3.348 4.506 5.525 6.452 7.336 -1.947 -0.055 1.558 2.941 4.142 5.208 6.188 7.130 8.081 -0.576 1.051 2.454 3.678 4.773 5.787 6.767 7.761 8.818 0.541 1.943 3.173 4.277 5.306 6.305 7.324 8.410 9.611 1.468 2.684 3.779 4.803 5.803 6.827 7.923 9.140 10.524 2.269 3.337 4.338 5.320 6.330 7.417 8.630 10.015 11.621 3.009 3.967 4.912 5.890 6.950 8.139 9.506 11.099 12.966 3.750 4.638 5.565 6.579 7.727 9.057 10.618 12.457 14.622 4.557 5.414 6.362 7.449 8.724 10.234 12.027 14.151 16.654 u(x,y,3) plane -2.363 -0.168 1.695 3.275 4.620 5.778 6.796 7.724 8.608 -0.950 0.942 2.555 3.938 5.138 6.205 7.185 8.126 9.078 0.146 1.773 3.175 4.399 5.494 6.508 7.488 8.482 9.539 0.987 2.389 3.619 4.724 5.752 6.751 7.770 8.856 10.057 1.639 2.855 3.951 4.974 5.974 6.998 8.095 9.311 10.695 2.166 3.234 4.234 5.216 6.226 7.314 8.526 9.911 11.518 2.630 3.589 4.533 5.511 6.571 7.761 9.128 10.721 12.587 3.097 3.985 4.912 5.925 7.073 8.403 9.964 11.803 13.969 3.629 4.486 5.434 6.521 7.796 9.305 11.099 13.223 15.726 u(x,y,4) plane -1.668 0.526 2.389 3.969 5.314 6.472 7.491 8.418 9.302 -0.421 1.471 3.084 4.467 5.668 6.734 7.714 8.656 9.607 0.510 2.137 3.539 4.763 5.858 6.872 7.852 8.847 9.904 1.187 2.589 3.818 4.923 5.951 6.950 7.969 9.055 10.257 1.674 2.889 3.985 5.008 6.008 7.032 8.129 9.345 10.730 2.035 3.103 4.103 5.085 6.095 7.183 8.395 9.780 11.387 2.335 3.293 4.237 5.215 6.275 7.465 8.832 10.425 12.292 2.636 3.524 4.451 5.464 6.612 7.942 9.503 11.343 13.508 3.003 3.860 4.808 5.895 7.170 8.680 10.473 12.597 15.101 u(x,y,5) plane -1.458 0.737 2.600 4.180 5.525 6.683 7.701 8.629 9.513 -0.265 1.626 3.240 4.622 5.823 6.889 7.869 8.811 9.763 0.610 2.238 3.639 4.864 5.959 6.972 7.952 8.947 10.004 1.232 2.634 3.863 4.968 5.996 6.996 8.014 9.101 10.302 1.664 2.880 3.975 4.999 5.999 7.023 8.119 9.336 10.720 1.971 3.038 4.039 5.020 6.031 7.118 8.331 9.716 11.322 2.215 3.174 4.118 5.096 6.156 7.345 8.712 10.305 12.172 2.462 3.350 4.277 5.290 6.438 7.768 9.329 11.168 13.334 2.774 3.631 4.579 5.666 6.940 8.450 10.243 12.368 14.871 u(x,y,6) plane -1.637 0.557 2.420 4.000 5.345 6.503 7.522 8.449 9.334 -0.389 1.502 3.115 4.498 5.699 6.765 7.745 8.687 9.638 0.541 2.168 3.570 4.795 5.890 6.903 7.883 8.878 9.935 1.218 2.620 3.849 4.954 5.982 6.981 8.000 9.086 10.288 1.705 2.920 4.016 5.040 6.039 7.064 8.160 9.376 10.761 2.066 3.134 4.134 5.116 6.126 7.214 8.426 9.812 11.418 2.366 3.324 4.269 5.247 6.306 7.496 8.863 10.456 12.323 2.667 3.556 4.482 5.496 6.643 7.974 9.534 11.374 13.540 3.035 3.891 4.839 5.927 7.201 8.711 10.504 12.628 15.132 u(x,y,7) plane -2.113 0.082 1.945 3.525 4.870 6.028 7.046 7.974 8.858 -0.700 1.192 2.805 4.188 5.388 6.455 7.435 8.376 9.328 0.396 2.023 3.425 4.649 5.744 6.758 7.738 8.732 9.789 1.237 2.639 3.869 4.974 6.002 7.001 8.020 9.106 10.307 1.889 3.105 4.201 5.224 6.224 7.248 8.345 9.561 10.945 2.416 3.484 4.484 5.466 6.476 7.564 8.776 10.161 11.768 2.880 3.839 4.783 5.761 6.821 8.011 9.378 10.971 12.837 3.347 4.235 5.162 6.175 7.323 8.653 10.214 12.053 14.219 3.879 4.736 5.684 6.771 8.046 9.555 11.349 13.473 15.976 u(x,y,8) plane -2.791 -0.596 1.267 2.847 4.192 5.350 6.368 7.296 8.180 -1.103 0.789 2.402 3.785 4.986 6.052 7.032 7.973 8.925 0.268 1.895 3.297 4.522 5.617 6.630 7.610 8.605 9.662 1.384 2.787 4.016 5.121 6.149 7.149 8.167 9.253 10.455 2.312 3.527 4.623 5.647 6.647 7.671 8.767 9.983 11.368 3.113 4.181 5.182 6.163 7.174 8.261 9.473 10.859 12.465 3.852 4.811 5.756 6.734 7.794 8.983 10.350 11.943 13.809 4.594 5.482 6.409 7.423 8.570 9.901 11.461 13.300 15.466 5.401 6.258 7.206 8.293 9.568 11.078 12.871 14.995 17.498 difference exact-computed solution u(x,y,2) plane 0.0001 0.0002 0.0002 0.0003 0.0003 0.0003 0.0002 0.0002 0.0001 0.0002 0.0003 0.0004 0.0005 0.0005 0.0005 0.0004 0.0003 0.0002 0.0002 0.0004 0.0006 0.0007 0.0007 0.0007 0.0006 0.0004 0.0002 0.0003 0.0005 0.0007 0.0008 0.0008 0.0008 0.0007 0.0005 0.0003 0.0003 0.0005 0.0007 0.0008 0.0009 0.0008 0.0007 0.0005 0.0003 0.0003 0.0005 0.0007 0.0008 0.0008 0.0008 0.0007 0.0005 0.0003 0.0002 0.0004 0.0006 0.0007 0.0007 0.0007 0.0006 0.0004 0.0002 0.0002 0.0003 0.0004 0.0005 0.0005 0.0005 0.0004 0.0003 0.0002 0.0001 0.0002 0.0002 0.0003 0.0003 0.0003 0.0002 0.0002 0.0001 u(x,y,3) plane 0.0002 0.0003 0.0004 0.0005 0.0005 0.0005 0.0004 0.0003 0.0002 0.0003 0.0006 0.0008 0.0009 0.0010 0.0009 0.0008 0.0006 0.0003 0.0004 0.0008 0.0011 0.0013 0.0013 0.0013 0.0011 0.0008 0.0004 0.0005 0.0009 0.0013 0.0015 0.0016 0.0015 0.0013 0.0009 0.0005 0.0005 0.0010 0.0013 0.0016 0.0016 0.0016 0.0013 0.0010 0.0005 0.0005 0.0009 0.0013 0.0015 0.0016 0.0015 0.0013 0.0009 0.0005 0.0004 0.0008 0.0011 0.0013 0.0013 0.0013 0.0011 0.0008 0.0004 0.0003 0.0006 0.0008 0.0009 0.0010 0.0009 0.0008 0.0006 0.0003 0.0002 0.0003 0.0004 0.0005 0.0005 0.0005 0.0004 0.0003 0.0002 u(x,y,4) plane 0.0002 0.0004 0.0005 0.0006 0.0007 0.0006 0.0005 0.0004 0.0002 0.0004 0.0007 0.0010 0.0012 0.0013 0.0012 0.0010 0.0007 0.0004 0.0005 0.0010 0.0014 0.0016 0.0017 0.0016 0.0014 0.0010 0.0005 0.0006 0.0012 0.0016 0.0019 0.0020 0.0019 0.0016 0.0012 0.0006 0.0007 0.0013 0.0017 0.0020 0.0021 0.0020 0.0017 0.0013 0.0007 0.0006 0.0012 0.0016 0.0019 0.0020 0.0019 0.0016 0.0012 0.0006 0.0005 0.0010 0.0014 0.0016 0.0017 0.0016 0.0014 0.0010 0.0005 0.0004 0.0007 0.0010 0.0012 0.0013 0.0012 0.0010 0.0007 0.0004 0.0002 0.0004 0.0005 0.0006 0.0007 0.0006 0.0005 0.0004 0.0002 u(x,y,5) plane 0.0002 0.0004 0.0006 0.0007 0.0007 0.0007 0.0006 0.0004 0.0002 0.0004 0.0008 0.0011 0.0013 0.0014 0.0013 0.0011 0.0008 0.0004 0.0006 0.0011 0.0015 0.0018 0.0019 0.0018 0.0015 0.0011 0.0006 0.0007 0.0013 0.0018 0.0021 0.0022 0.0021 0.0018 0.0013 0.0007 0.0007 0.0014 0.0019 0.0022 0.0023 0.0022 0.0019 0.0014 0.0007 0.0007 0.0013 0.0018 0.0021 0.0022 0.0021 0.0018 0.0013 0.0007 0.0006 0.0011 0.0015 0.0018 0.0019 0.0018 0.0015 0.0011 0.0006 0.0004 0.0008 0.0011 0.0013 0.0014 0.0013 0.0011 0.0008 0.0004 0.0002 0.0004 0.0006 0.0007 0.0007 0.0007 0.0006 0.0004 0.0002 u(x,y,6) plane 0.0002 0.0004 0.0005 0.0006 0.0007 0.0006 0.0005 0.0004 0.0002 0.0004 0.0007 0.0010 0.0012 0.0013 0.0012 0.0010 0.0007 0.0004 0.0005 0.0010 0.0014 0.0016 0.0017 0.0016 0.0014 0.0010 0.0005 0.0006 0.0012 0.0016 0.0019 0.0020 0.0019 0.0016 0.0012 0.0006 0.0007 0.0013 0.0017 0.0020 0.0021 0.0020 0.0017 0.0013 0.0007 0.0006 0.0012 0.0016 0.0019 0.0020 0.0019 0.0016 0.0012 0.0006 0.0005 0.0010 0.0014 0.0016 0.0017 0.0016 0.0014 0.0010 0.0005 0.0004 0.0007 0.0010 0.0012 0.0013 0.0012 0.0010 0.0007 0.0004 0.0002 0.0004 0.0005 0.0006 0.0007 0.0006 0.0005 0.0004 0.0002 u(x,y,7) plane 0.0002 0.0003 0.0004 0.0005 0.0005 0.0005 0.0004 0.0003 0.0002 0.0003 0.0006 0.0008 0.0009 0.0010 0.0009 0.0008 0.0006 0.0003 0.0004 0.0008 0.0011 0.0013 0.0013 0.0013 0.0011 0.0008 0.0004 0.0005 0.0009 0.0013 0.0015 0.0016 0.0015 0.0013 0.0009 0.0005 0.0005 0.0010 0.0013 0.0016 0.0016 0.0016 0.0013 0.0010 0.0005 0.0005 0.0009 0.0013 0.0015 0.0016 0.0015 0.0013 0.0009 0.0005 0.0004 0.0008 0.0011 0.0013 0.0013 0.0013 0.0011 0.0008 0.0004 0.0003 0.0006 0.0008 0.0009 0.0010 0.0009 0.0008 0.0006 0.0003 0.0002 0.0003 0.0004 0.0005 0.0005 0.0005 0.0004 0.0003 0.0002 u(x,y,8) plane 0.0001 0.0002 0.0002 0.0003 0.0003 0.0003 0.0002 0.0002 0.0001 0.0002 0.0003 0.0004 0.0005 0.0005 0.0005 0.0004 0.0003 0.0002 0.0002 0.0004 0.0006 0.0007 0.0007 0.0007 0.0006 0.0004 0.0002 0.0003 0.0005 0.0007 0.0008 0.0008 0.0008 0.0007 0.0005 0.0003 0.0003 0.0005 0.0007 0.0008 0.0009 0.0008 0.0007 0.0005 0.0003 0.0003 0.0005 0.0007 0.0008 0.0008 0.0008 0.0007 0.0005 0.0003 0.0002 0.0004 0.0006 0.0007 0.0007 0.0007 0.0006 0.0004 0.0002 0.0002 0.0003 0.0004 0.0005 0.0005 0.0005 0.0004 0.0003 0.0002 0.0001 0.0002 0.0002 0.0003 0.0003 0.0003 0.0002 0.0002 0.0001