pde3b.f90 running xmin= -1.00000000000000 xmax= 1.20000004768372 nx= 10 hx= 0.220000004768372 ymin= -1.00000000000000 ymax= 1.00000000000000 ny= 10 hy= 0.200000000000000 zmin= -1.00000000000000 zmax= 1.00000000000000 nz= 8 hz= 0.250000000000000 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=2542.9857 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=1222.8350 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= 897.8236 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, 0 ) 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, 1 ) 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 -3.658 -1.486 0.360 1.928 3.268 4.429 5.458 6.403 7.311 8.225 -4.165 -1.992 -0.142 1.438 2.798 3.989 5.061 6.062 7.037 8.032 9.090 -2.477 -0.639 0.931 2.287 3.480 4.562 5.583 6.591 7.633 8.750 9.985 -1.082 0.466 1.801 2.975 4.043 5.056 6.064 7.117 8.258 9.531 10.975 0.084 1.389 2.533 3.570 4.555 5.538 6.572 7.704 8.979 10.439 12.124 1.086 2.194 3.193 4.137 5.081 6.076 7.173 8.420 9.861 11.540 13.496 1.987 2.944 3.844 4.740 5.686 6.733 7.930 9.327 10.968 12.896 15.154 2.852 3.703 4.548 5.440 6.430 7.568 8.904 10.486 12.361 14.571 17.162 3.744 4.532 5.366 6.296 7.371 8.640 10.153 11.958 14.100 16.628 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, 2 ) 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 -2.407 -0.253 1.578 3.136 4.472 5.635 6.674 7.634 8.561 9.497 -3.168 -1.034 0.781 2.332 3.672 4.856 5.933 6.951 7.955 8.987 10.087 -1.756 0.029 1.551 2.866 4.032 5.104 6.132 7.164 8.245 9.414 10.707 -0.636 0.850 2.127 3.254 4.289 5.289 6.306 7.387 8.576 9.909 11.422 0.256 1.494 2.577 3.564 4.515 5.485 6.527 7.689 9.014 10.539 12.296 0.983 2.026 2.967 3.864 4.775 5.757 6.862 8.138 9.627 11.367 13.393 1.609 2.511 3.360 4.216 5.134 6.170 7.374 8.796 10.477 12.459 14.776 2.199 3.009 3.818 4.680 5.650 6.780 8.121 9.721 11.625 13.875 16.509 2.815 3.583 4.398 5.312 6.376 7.641 9.157 10.970 13.129 15.677 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, 3 ) 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 -1.726 0.416 2.236 3.787 5.120 6.285 7.330 8.301 9.240 10.192 -2.638 -0.530 1.261 2.792 4.120 5.298 6.378 7.408 8.431 9.488 10.616 -1.391 0.358 1.846 3.135 4.283 5.347 6.380 7.429 8.536 9.740 11.071 -0.436 1.007 2.245 3.340 4.355 5.346 6.368 7.468 8.688 10.063 11.621 0.290 1.483 2.525 3.479 4.407 5.368 6.416 7.599 8.957 10.524 12.330 0.852 1.853 2.754 3.619 4.509 5.482 6.592 7.888 9.409 11.190 13.262 1.314 2.178 2.994 3.822 4.722 5.750 6.959 8.397 10.107 12.123 14.480 1.738 2.522 3.306 4.148 5.104 6.229 7.573 9.186 11.110 13.385 16.049 2.190 2.943 3.745 4.648 5.705 6.968 8.485 10.305 12.474 15.036 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, 4 ) 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 -1.520 0.617 2.434 3.983 5.315 6.480 7.527 8.501 9.446 10.402 -2.483 -0.384 1.399 2.923 4.246 5.423 6.504 7.538 8.568 9.634 10.772 -1.291 0.446 1.923 3.202 4.344 5.405 6.439 7.494 8.611 9.827 11.172 -0.391 1.037 2.262 3.346 4.353 5.341 6.365 7.472 8.703 10.092 11.667 0.281 1.458 2.485 3.427 4.347 5.305 6.355 7.545 8.915 10.498 12.321 0.788 1.773 2.660 3.514 4.396 5.366 6.479 7.781 9.313 11.109 13.198 1.194 2.046 2.850 3.668 4.562 5.587 6.798 8.242 9.961 11.990 14.361 1.564 2.338 3.113 3.948 4.900 6.022 7.368 8.985 10.916 13.201 15.874 1.960 2.709 3.506 4.405 5.460 6.721 8.239 10.062 12.235 14.801 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, 5 ) 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 -1.695 0.447 2.267 3.818 5.151 6.316 7.361 8.332 9.271 10.223 -2.607 -0.499 1.292 2.823 4.150 5.329 6.409 7.438 8.462 9.519 10.647 -1.360 0.389 1.877 3.166 4.314 5.378 6.410 7.459 8.567 9.771 11.103 -0.405 1.038 2.275 3.371 4.385 5.376 6.398 7.499 8.719 10.094 11.653 0.322 1.514 2.555 3.509 4.437 5.398 6.446 7.629 8.987 10.555 12.362 0.884 1.884 2.784 3.649 4.539 5.512 6.623 7.918 9.439 11.221 13.293 1.345 2.209 3.025 3.853 4.752 5.780 6.990 8.428 10.137 12.154 14.511 1.769 2.553 3.337 4.179 5.135 6.259 7.604 9.217 11.141 13.416 16.080 2.221 2.974 3.776 4.679 5.736 6.998 8.516 10.336 12.505 15.067 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, 6 ) 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 -2.157 -0.003 1.827 3.385 4.721 5.885 6.923 7.884 8.810 9.747 -2.918 -0.784 1.030 2.581 3.921 5.105 6.182 7.200 8.204 9.237 10.337 -1.506 0.279 1.800 3.115 4.281 5.352 6.380 7.413 8.494 9.664 10.957 -0.386 1.099 2.376 3.502 4.538 5.538 6.554 7.636 8.825 10.159 11.672 0.506 1.743 2.825 3.812 4.763 5.733 6.776 7.938 9.263 10.788 12.546 1.233 2.276 3.216 4.112 5.024 6.006 7.111 8.387 9.876 11.617 13.643 1.859 2.760 3.610 4.465 5.383 6.418 7.623 9.044 10.726 12.708 15.026 2.449 3.259 4.068 4.929 5.899 7.029 8.370 9.971 11.875 14.125 16.759 3.065 3.833 4.647 5.561 6.625 7.890 9.406 11.220 13.379 15.927 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, 7 ) 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 -2.815 -0.642 1.203 2.771 4.112 5.272 6.302 7.247 8.154 9.069 -3.321 -1.149 0.701 2.281 3.641 4.832 5.904 6.905 7.880 8.875 9.933 -1.634 0.204 1.774 3.129 4.322 5.404 6.426 7.434 8.476 9.593 10.829 -0.239 1.310 2.644 3.818 4.885 5.898 6.907 7.959 9.101 10.374 11.819 0.928 2.232 3.376 4.413 5.397 6.381 7.415 8.547 9.822 11.282 12.968 1.930 3.037 4.036 4.980 5.924 6.919 8.016 9.263 10.704 12.383 14.339 2.831 3.787 4.687 5.583 6.529 7.575 8.773 10.170 11.811 13.740 15.998 3.696 4.546 5.391 6.283 7.273 8.411 9.747 11.329 13.204 15.415 18.006 4.587 5.376 6.210 7.139 8.214 9.484 10.997 12.801 14.944 17.471 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, 8 ) 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 difference exact-computed solution u(x,y, 0 ) plane 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 u(x,y, 1 ) 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, 2 ) 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, 3 ) 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, 4 ) 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, 5 ) 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, 6 ) 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, 7 ) 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 u(x,y, 8 ) plane 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 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= 0.2329 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, 0 ) 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, 1 ) 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 -3.636 -1.443 0.420 1.999 3.344 4.502 5.521 6.450 7.335 8.225 -4.165 -1.949 -0.060 1.552 2.934 4.134 5.200 6.181 7.125 8.078 9.090 -2.477 -0.580 1.045 2.444 3.667 4.762 5.776 6.757 7.754 8.814 9.985 -1.082 0.537 1.935 3.162 4.265 5.292 6.292 7.313 8.402 9.607 10.975 0.084 1.464 2.675 3.768 4.790 5.789 6.814 7.912 9.131 10.520 12.124 1.086 2.265 3.329 4.327 5.307 6.317 7.405 8.619 10.007 11.617 13.496 1.987 3.005 3.961 4.903 5.879 6.938 8.129 9.497 11.093 12.962 15.154 2.852 3.747 4.634 5.559 6.571 7.718 9.049 10.611 12.452 14.620 17.162 3.744 4.556 5.412 6.359 7.445 8.720 10.230 12.023 14.148 16.653 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, 2 ) 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 -2.365 -0.173 1.688 3.267 4.612 5.770 6.790 7.719 8.606 9.497 -3.168 -0.955 0.933 2.543 3.923 5.123 6.190 7.172 8.117 9.073 10.087 -1.756 0.139 1.761 3.158 4.379 5.473 6.488 7.471 8.470 9.533 10.707 -0.636 0.980 2.375 3.599 4.700 5.727 6.728 7.750 8.842 10.050 11.422 0.256 1.631 2.840 3.930 4.950 5.948 6.974 8.074 9.296 10.687 12.296 0.983 2.158 3.219 4.214 5.192 6.202 7.290 8.506 9.897 11.510 13.393 1.609 2.624 3.577 4.516 5.491 6.550 7.741 9.111 10.708 12.581 14.776 2.199 3.092 3.976 4.900 5.911 7.058 8.389 9.952 11.794 13.964 16.509 2.815 3.627 4.481 5.427 6.514 7.788 9.298 11.092 13.218 15.724 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, 3 ) 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 -1.672 0.520 2.381 3.959 5.304 6.462 7.482 8.412 9.299 10.192 -2.638 -0.427 1.459 3.068 4.448 5.648 6.715 7.698 8.644 9.601 10.616 -1.391 0.501 2.121 3.517 4.737 5.831 6.846 7.830 8.830 9.895 11.071 -0.436 1.177 2.570 3.792 4.892 5.918 6.919 7.943 9.036 10.247 11.621 0.290 1.663 2.869 3.957 4.976 5.974 7.000 8.101 9.325 10.719 12.330 0.852 2.025 3.084 4.077 5.054 6.063 7.152 8.369 9.761 11.377 13.262 1.314 2.326 3.277 4.215 5.189 6.248 7.439 8.810 10.409 12.283 14.480 1.738 2.630 3.513 4.435 5.445 6.592 7.923 9.487 11.331 13.502 16.049 2.190 3.000 3.854 4.800 5.885 7.159 8.670 10.464 12.591 15.097 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, 4 ) 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 -1.461 0.730 2.591 4.169 5.513 6.672 7.692 8.622 9.510 10.402 -2.483 -0.272 1.614 3.222 4.602 5.801 6.869 7.852 8.798 9.756 10.772 -1.291 0.601 2.220 3.616 4.836 5.929 6.944 7.928 8.930 9.995 11.172 -0.391 1.221 2.614 3.835 4.935 5.961 6.962 7.986 9.080 10.291 11.667 0.281 1.653 2.858 3.945 4.964 5.962 6.988 8.089 9.314 10.709 12.321 0.788 1.960 3.018 4.010 4.987 5.996 7.085 8.302 9.695 11.312 13.198 1.194 2.206 3.156 4.094 5.068 6.126 7.317 8.688 10.288 12.163 14.361 1.564 2.455 3.337 4.259 5.269 6.416 7.747 9.311 11.155 13.327 15.874 1.960 2.770 3.624 4.570 5.655 6.929 8.439 10.234 12.361 14.868 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, 5 ) 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 -1.640 0.551 2.412 3.991 5.335 6.493 7.513 8.443 9.330 10.223 -2.607 -0.395 1.490 3.099 4.479 5.679 6.746 7.729 8.675 9.632 10.647 -1.360 0.533 2.152 3.548 4.769 5.862 6.877 7.861 8.862 9.926 11.103 -0.405 1.208 2.601 3.823 4.923 5.950 6.951 7.974 9.067 10.278 11.653 0.322 1.695 2.900 3.988 5.007 6.006 7.031 8.132 9.356 10.750 12.362 0.884 2.056 3.115 4.108 5.085 6.094 7.183 8.400 9.793 11.408 13.293 1.345 2.357 3.308 4.246 5.220 6.279 7.470 8.841 10.440 12.314 14.511 1.769 2.661 3.544 4.466 5.477 6.623 7.955 9.518 11.362 13.533 16.080 2.221 3.031 3.885 4.831 5.917 7.191 8.701 10.496 12.622 15.129 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, 6 ) 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 -2.115 0.077 1.938 3.517 4.862 6.020 7.040 7.969 8.856 9.747 -2.918 -0.705 1.183 2.793 4.173 5.373 6.440 7.422 8.367 9.323 10.337 -1.506 0.389 2.011 3.408 4.629 5.723 6.738 7.721 8.720 9.783 10.957 -0.386 1.230 2.625 3.849 4.950 5.977 6.978 8.000 9.092 10.300 11.672 0.506 1.881 3.090 4.180 5.200 6.198 7.224 8.324 9.546 10.937 12.546 1.233 2.408 3.469 4.464 5.442 6.452 7.540 8.756 10.147 11.760 13.643 1.859 2.874 3.827 4.766 5.741 6.800 7.991 9.361 10.958 12.831 15.026 2.449 3.342 4.226 5.150 6.161 7.308 8.639 10.202 12.044 14.214 16.759 3.065 3.877 4.731 5.677 6.764 8.038 9.548 11.342 13.468 15.974 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, 7 ) 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 -2.792 -0.599 1.263 2.843 4.188 5.346 6.365 7.293 8.179 9.069 -3.321 -1.105 0.784 2.395 3.777 4.977 6.044 7.025 7.969 8.922 9.933 -1.634 0.264 1.889 3.288 4.511 5.606 6.620 7.601 8.598 9.658 10.829 -0.239 1.380 2.779 4.006 5.108 6.136 7.136 8.157 9.245 10.450 11.819 0.928 2.307 3.519 4.612 5.634 6.633 7.658 8.756 9.975 11.363 12.968 1.930 3.109 4.173 5.171 6.151 7.160 8.248 9.463 10.851 12.460 14.339 2.831 3.849 4.805 5.746 6.723 7.782 8.972 10.341 11.936 13.806 15.998 3.696 4.591 5.477 6.402 7.415 8.562 9.893 11.455 13.296 15.463 18.006 4.587 5.400 6.255 7.202 8.289 9.563 11.073 12.867 14.992 17.497 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, 8 ) 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 difference exact-computed solution u(x,y, 0 ) plane 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 u(x,y, 1 ) 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, 2 ) 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, 3 ) 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, 4 ) 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, 5 ) 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, 6 ) 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, 7 ) 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, 8 ) plane 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 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, 0 ) 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, 1 ) 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, 2 ) 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, 3 ) 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, 4 ) 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, 5 ) 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, 6 ) 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, 7 ) 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, 8 ) 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, 0 ) 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, 1 ) 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 -3.635 -1.440 0.423 2.003 3.348 4.506 5.525 6.452 7.336 8.225 -4.165 -1.947 -0.055 1.558 2.941 4.142 5.208 6.188 7.130 8.081 9.090 -2.477 -0.576 1.051 2.454 3.678 4.773 5.787 6.767 7.761 8.818 9.985 -1.082 0.541 1.943 3.173 4.277 5.306 6.305 7.324 8.410 9.611 10.975 0.084 1.468 2.684 3.779 4.803 5.803 6.827 7.923 9.140 10.524 12.124 1.086 2.269 3.337 4.338 5.320 6.330 7.417 8.630 10.015 11.621 13.496 1.987 3.009 3.967 4.912 5.890 6.950 8.139 9.506 11.099 12.966 15.154 2.852 3.750 4.638 5.565 6.579 7.727 9.057 10.618 12.457 14.622 17.162 3.744 4.557 5.414 6.362 7.449 8.724 10.234 12.027 14.151 16.654 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, 2 ) 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 6.796 7.724 8.608 9.497 -3.168 -0.950 0.942 2.555 3.938 5.138 6.205 7.185 8.126 9.078 10.087 -1.756 0.146 1.773 3.175 4.399 5.494 6.508 7.488 8.482 9.539 10.707 -0.636 0.987 2.389 3.619 4.724 5.752 6.751 7.770 8.856 10.057 11.422 0.256 1.639 2.855 3.951 4.974 5.974 6.998 8.095 9.311 10.695 12.296 0.983 2.166 3.234 4.234 5.216 6.226 7.314 8.526 9.911 11.518 13.393 1.609 2.630 3.589 4.533 5.511 6.571 7.761 9.128 10.721 12.587 14.776 2.199 3.097 3.985 4.912 5.925 7.073 8.403 9.964 11.803 13.969 16.509 2.815 3.629 4.486 5.434 6.521 7.796 9.305 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, 3 ) 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 2.389 3.969 5.314 6.472 7.491 8.418 9.302 10.192 -2.638 -0.421 1.471 3.084 4.467 5.668 6.734 7.714 8.656 9.607 10.616 -1.391 0.510 2.137 3.539 4.763 5.858 6.872 7.852 8.847 9.904 11.071 -0.436 1.187 2.589 3.818 4.923 5.951 6.950 7.969 9.055 10.257 11.621 0.290 1.674 2.889 3.985 5.008 6.008 7.032 8.129 9.345 10.730 12.330 0.852 2.035 3.103 4.103 5.085 6.095 7.183 8.395 9.780 11.387 13.262 1.314 2.335 3.293 4.237 5.215 6.275 7.465 8.832 10.425 12.292 14.480 1.738 2.636 3.524 4.451 5.464 6.612 7.942 9.503 11.343 13.508 16.049 2.190 3.003 3.860 4.808 5.895 7.170 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, 4 ) 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 7.701 8.629 9.513 10.402 -2.483 -0.265 1.626 3.240 4.622 5.823 6.889 7.869 8.811 9.763 10.772 -1.291 0.610 2.238 3.639 4.864 5.959 6.972 7.952 8.947 10.004 11.172 -0.391 1.232 2.634 3.863 4.968 5.996 6.996 8.014 9.101 10.302 11.667 0.281 1.664 2.880 3.975 4.999 5.999 7.023 8.119 9.336 10.720 12.321 0.788 1.971 3.038 4.039 5.020 6.031 7.118 8.331 9.716 11.322 13.198 1.194 2.215 3.174 4.118 5.096 6.156 7.345 8.712 10.305 12.172 14.361 1.564 2.462 3.350 4.277 5.290 6.438 7.768 9.329 11.168 13.334 15.874 1.960 2.774 3.631 4.579 5.666 6.940 8.450 10.243 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, 5 ) 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 0.557 2.420 4.000 5.345 6.503 7.522 8.449 9.334 10.223 -2.607 -0.389 1.502 3.115 4.498 5.699 6.765 7.745 8.687 9.638 10.647 -1.360 0.541 2.168 3.570 4.795 5.890 6.903 7.883 8.878 9.935 11.103 -0.405 1.218 2.620 3.849 4.954 5.982 6.981 8.000 9.086 10.288 11.653 0.322 1.705 2.920 4.016 5.040 6.039 7.064 8.160 9.376 10.761 12.362 0.884 2.066 3.134 4.134 5.116 6.126 7.214 8.426 9.812 11.418 13.293 1.345 2.366 3.324 4.269 5.247 6.306 7.496 8.863 10.456 12.323 14.511 1.769 2.667 3.556 4.482 5.496 6.643 7.974 9.534 11.374 13.540 16.080 2.221 3.035 3.891 4.839 5.927 7.201 8.711 10.504 12.628 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, 6 ) 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 7.046 7.974 8.858 9.747 -2.918 -0.700 1.192 2.805 4.188 5.388 6.455 7.435 8.376 9.328 10.337 -1.506 0.396 2.023 3.425 4.649 5.744 6.758 7.738 8.732 9.789 10.957 -0.386 1.237 2.639 3.869 4.974 6.002 7.001 8.020 9.106 10.307 11.672 0.506 1.889 3.105 4.201 5.224 6.224 7.248 8.345 9.561 10.945 12.546 1.233 2.416 3.484 4.484 5.466 6.476 7.564 8.776 10.161 11.768 13.643 1.859 2.880 3.839 4.783 5.761 6.821 8.011 9.378 10.971 12.837 15.026 2.449 3.347 4.235 5.162 6.175 7.323 8.653 10.214 12.053 14.219 16.759 3.065 3.879 4.736 5.684 6.771 8.046 9.555 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, 7 ) 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 6.368 7.296 8.180 9.069 -3.321 -1.103 0.789 2.402 3.785 4.986 6.052 7.032 7.973 8.925 9.933 -1.634 0.268 1.895 3.297 4.522 5.617 6.630 7.610 8.605 9.662 10.829 -0.239 1.384 2.787 4.016 5.121 6.149 7.149 8.167 9.253 10.455 11.819 0.928 2.312 3.527 4.623 5.647 6.647 7.671 8.767 9.983 11.368 12.968 1.930 3.113 4.181 5.182 6.163 7.174 8.261 9.473 10.859 12.465 14.339 2.831 3.852 4.811 5.756 6.734 7.794 8.983 10.350 11.943 13.809 15.998 3.696 4.594 5.482 6.409 7.423 8.570 9.901 11.461 13.300 15.466 18.006 4.587 5.401 6.258 7.206 8.293 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, 8 ) 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 difference exact-computed solution u(x,y, 0 ) plane 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 u(x,y, 1 ) 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, 2 ) 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, 3 ) 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, 4 ) 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, 5 ) 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, 6 ) 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, 7 ) 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, 8 ) plane 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000