pdenu_eq.f90 running differential equation to solve d^2u/dx^2 + 2*d^2u/dy^2 + 3*d^2u/dxdy + 4*du/dx + 5*du/dy +6*u = c(x,y) c(x,y) = 6x^3+12y^3+18x^2y+24xy^2+57x^2+82y^2+64xy+122x+114y+110 non uniform grid on rectangle -1.0,-1.1 to 1.2,1.3 known solution to test method u(x,y) = x^3+2y^3+3x^2y+4xy^2+5x^2+6y^2+7x+8 xmin= -1.00000000000000 xmax= 1.20000004768372 nx= 10 ymin= -1.10000002384186 ymax= 1.29999995231628 ny= 9 u(xg(0),yg(0))= -2.59322427650660 c(xg(0),yg(0))= 7.46848582978080 internal cells zeroed matrix initialized initial matrix, left side, upper -642.540 278.407 -23.184 4.836 -1.906 0.874 -0.608 0.402 -39.414 -420.674 131.126 -35.667 18.411 -10.780 8.870 -6.443 51.959 -85.252 -354.928 79.891 -30.805 16.036 -12.552 8.918 -30.762 48.848 -49.368 -369.701 73.845 -25.330 17.412 -11.753 27.568 -42.231 39.705 -52.234 -347.951 64.317 -32.720 20.166 -20.825 31.038 -27.169 30.518 -40.614 -368.783 86.492 -38.498 14.678 -21.571 18.238 -18.971 22.486 -30.771 -401.456 109.671 -21.878 31.984 -26.710 27.092 -30.943 41.746 -73.656 -375.642 initial matrix, right side, upper 1.828 -0.748 0.434 -0.270 0.229 -0.169 0.064 674.267 -1.982 0.649 -0.353 0.212 -0.177 0.130 -0.049 375.701 -5.319 -1.462 0.636 -0.348 0.278 -0.199 0.074 341.921 2.183 -4.348 -1.555 0.621 -0.447 0.307 -0.111 222.852 -1.254 2.053 -4.807 -1.325 0.750 -0.477 0.166 153.533 0.915 -1.095 1.770 -4.255 -1.878 0.937 -0.295 66.484 -0.662 0.713 -0.906 1.699 -3.869 -2.229 0.521 34.672 0.686 -0.708 0.833 -1.226 3.222 -5.481 -1.463 6.374 initial matrix, right side, lower 53.703 -10.317 4.623 -2.481 1.950 -1.385 0.510 -15.811 -324.075 22.778 -5.954 2.457 -1.701 1.138 -0.404 -38.961 35.871 -301.144 13.125 -1.083 -0.031 0.231 -0.125 -78.344 -9.268 27.941 -297.553 12.573 -3.427 1.535 -0.425 -143.735 8.581 -12.251 28.509 -297.108 13.135 -1.891 0.087 -237.458 -7.604 8.862 -12.915 35.592 -314.924 22.625 -1.123 -340.679 0.075 -0.553 1.606 -6.129 52.179 -352.190 39.992 -393.968 46.140 -45.660 50.166 -62.147 99.214 -68.464 -273.506 -501.430 exact solution u, computed us, error xg=-0.900, yg=-1.000, u=-2.328, us= -2.328err= 0.9769013E-08 xg=-0.900, yg=-0.900, u=-2.189, us= -2.189err= 0.3488301E-07 xg=-0.900, yg=-0.600, u=-1.712, us= -1.712err= -0.1111380E-06 xg=-0.900, yg=-0.200, u=-1.067, us= -1.067err= 0.1975456E-06 xg=-0.900, yg= 0.300, u=-0.431, us= -0.431err= -0.2472464E-06 xg=-0.900, yg= 0.800, u=-0.049, us= -0.049err= 0.6672722E-07 xg=-0.900, yg= 1.000, u= 0.041, us= 0.041err= 0.8669341E-07 xg=-0.900, yg= 1.200, u= 0.100, us= 0.100err= 0.7018079E-07 xg=-0.800, yg=-1.000, u=-2.167, us= -2.167err= 0.1328397E-07 xg=-0.800, yg=-0.900, u=-2.037, us= -2.037err= -0.2381962E-07 xg=-0.800, yg=-0.600, u=-1.593, us= -1.593err= -0.4762955E-07 xg=-0.800, yg=-0.200, u=-0.987, us= -0.987err= 0.2136492E-06 xg=-0.800, yg= 0.300, u=-0.377, us= -0.377err= -0.3633578E-06 xg=-0.800, yg= 0.800, u= 0.000, us= -0.000err= 0.1932545E-06 xg=-0.800, yg= 1.000, u= 0.089, us= 0.089err= 0.1173008E-06 xg=-0.800, yg= 1.200, u= 0.149, us= 0.149err= 0.3772945E-07 xg=-0.600, yg=-1.000, u=-1.821, us= -1.821err= -0.3113235E-07 xg=-0.600, yg=-0.900, u=-1.712, us= -1.712err= -0.4186597E-07 xg=-0.600, yg=-0.600, u=-1.336, us= -1.336err= 0.1979499E-06 xg=-0.600, yg=-0.200, u=-0.809, us= -0.809err= -0.1909313E-06 xg=-0.600, yg= 0.300, u=-0.247, us= -0.247err= -0.4961906E-07 xg=-0.600, yg= 0.800, u= 0.123, us= 0.123err= 0.1829129E-06 xg=-0.600, yg= 1.000, u= 0.214, us= 0.214err= -0.2488091E-07 xg=-0.600, yg= 1.200, u= 0.275, us= 0.275err= -0.2592902E-07 xg=-0.300, yg=-1.000, u=-1.301, us= -1.301err= 0.3948307E-07 xg=-0.300, yg=-0.900, u=-1.221, us= -1.221err= 0.8443249E-07 xg=-0.300, yg=-0.600, u=-0.938, us= -0.938err= -0.1272824E-06 xg=-0.300, yg=-0.200, u=-0.509, us= -0.509err= -0.2268564E-06 xg=-0.300, yg= 0.300, u= 0.000, us= -0.000err= 0.3502808E-06 xg=-0.300, yg= 0.800, u= 0.377, us= 0.377err= -0.1417740E-06 xg=-0.300, yg= 1.000, u= 0.477, us= 0.477err= -0.4779134E-08 xg=-0.300, yg= 1.200, u= 0.547, us= 0.547err= 0.4862791E-07 xg= 0.000, yg=-1.000, u=-0.841, us= -0.841err= -0.2772726E-07 xg= 0.000, yg=-0.900, u=-0.783, us= -0.783err= -0.1027122E-06 xg= 0.000, yg=-0.600, u=-0.565, us= -0.565err= -0.1589983E-06 xg= 0.000, yg=-0.200, u=-0.199, us= -0.199err= 0.3280238E-06 xg= 0.000, yg= 0.300, u= 0.296, us= 0.296err= -0.1898285E-06 xg= 0.000, yg= 0.800, u= 0.717, us= 0.717err= 0.2036159E-06 xg= 0.000, yg= 1.000, u= 0.841, us= 0.841err= 0.1612816E-06 xg= 0.000, yg= 1.200, u= 0.932, us= 0.932err= -0.4390040E-07 xg= 0.350, yg=-1.000, u=-0.426, us= -0.426err= -0.6250595E-08 xg= 0.350, yg=-0.900, u=-0.381, us= -0.381err= 0.4151171E-07 xg= 0.350, yg=-0.600, u=-0.201, us= -0.201err= 0.3003516E-06 xg= 0.350, yg=-0.200, u= 0.139, us= 0.139err= -0.2837672E-06 xg= 0.350, yg= 0.300, u= 0.672, us= 0.672err= 0.2065735E-06 xg= 0.350, yg= 0.800, u= 1.208, us= 1.208err= -0.3256161E-06 xg= 0.350, yg= 1.000, u= 1.385, us= 1.385err= -0.5815063E-06 xg= 0.350, yg= 1.200, u= 1.522, us= 1.522err= -0.1839107E-06 xg= 0.650, yg=-1.000, u=-0.179, us= -0.179err= 0.6833304E-07 xg= 0.650, yg=-0.900, u=-0.138, us= -0.138err= 0.1197014E-06 xg= 0.650, yg=-0.600, u= 0.034, us= 0.034err= -0.3402153E-06 xg= 0.650, yg=-0.200, u= 0.382, us= 0.382err= -0.2079863E-06 xg= 0.650, yg= 0.300, u= 0.989, us= 0.989err= 0.1302348E-06 xg= 0.650, yg= 0.800, u= 1.670, us= 1.670err= -0.8134318E-06 xg= 0.650, yg= 1.000, u= 1.910, us= 1.910err= 0.8412763E-07 xg= 0.650, yg= 1.200, u= 2.097, us= 2.097err= 0.3103399E-06 xg= 0.850, yg=-1.000, u=-0.064, us= -0.064err= -0.6846673E-07 xg= 0.850, yg=-0.900, u=-0.023, us= -0.023err= -0.1928138E-06 xg= 0.850, yg=-0.600, u= 0.149, us= 0.149err= -0.7163270E-06 xg= 0.850, yg=-0.200, u= 0.511, us= 0.511err= 0.5767155E-06 xg= 0.850, yg= 0.300, u= 1.178, us= 1.178err= -0.1070759E-05 xg= 0.850, yg= 0.800, u= 1.968, us= 1.968err= 0.4894798E-06 xg= 0.850, yg= 1.000, u= 2.249, us= 2.249err= 0.9386831E-06 xg= 0.850, yg= 1.200, u= 2.461, us= 2.461err= 0.1532257E-06 xg= 1.000, yg=-1.000, u= 0.000, us= 0.000err= -0.2447395E-06 xg= 1.000, yg=-0.900, u= 0.041, us= 0.041err= -0.4569040E-06 xg= 1.000, yg=-0.600, u= 0.214, us= 0.214err= -0.4813296E-06 xg= 1.000, yg=-0.200, u= 0.587, us= 0.587err= 0.7592139E-06 xg= 1.000, yg= 0.300, u= 1.301, us= 1.301err= -0.1509283E-05 xg= 1.000, yg= 0.800, u= 2.167, us= 2.167err= 0.1361081E-05 xg= 1.000, yg= 1.000, u= 2.472, us= 2.472err= 0.4555244E-06 xg= 1.000, yg= 1.200, u= 2.684, us= 2.684err= -0.2633293E-06 error= 0.18560767E-04 avg= 0.25778843E-06 max= 0.15092828E-05