pdenu22_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))= 1.45799986028671 c(xg(0),yg(0))= 18.4080003824234 internal cells zeroed cxx 82.5822964982437 -133.649208183429 24.0569073106531 39.5360061350502 -20.8334064201593 12.9865608290091 -8.40375605306397 7.25784374314605 -5.39303985900461 2.04416984657119 -0.184373847017172 matrix initialized initial matrix, left side, upper -354.582 -188.806 92.026 -42.316 25.450 -16.168 13.841 -10.243 204.886 -561.055 6.162 5.249 -3.843 2.615 -2.299 1.721 -58.121 143.095 -448.672 -12.291 9.306 -5.882 4.962 -3.640 36.478 -62.738 88.211 -400.795 -24.159 13.806 -10.741 7.589 -23.942 37.908 -39.340 77.172 -406.560 -19.199 14.560 -9.905 22.041 -33.397 30.533 -38.513 70.953 -390.957 -31.910 20.588 -18.202 27.036 -23.473 25.953 -34.653 76.341 -397.855 -30.825 13.137 -19.374 16.523 -17.528 21.592 -35.525 129.446 -472.659 initial matrix, right side, upper -1.828 0.748 -0.434 0.270 -0.229 0.169 -0.064 -420.410 1.982 -0.649 0.353 -0.212 0.177 -0.130 0.049 -542.846 -2.270 1.462 -0.636 0.348 -0.278 0.199 -0.074 -867.156 -2.183 -3.295 1.555 -0.621 0.447 -0.307 0.111-1415.276 1.254 -2.053 -2.889 1.325 -0.750 0.477 -0.166-1955.651 -0.915 1.095 -1.770 -3.503 1.878 -0.937 0.295-2636.741 0.662 -0.713 0.906 -1.699 -3.943 2.229 -0.521-3330.648 -0.686 0.708 -0.833 1.226 -3.222 -2.367 1.463-3745.891 initial matrix, right side, lower 91.723 -22.765 11.394 -6.556 5.348 -3.868 1.442-2795.128 -290.897 50.824 -18.157 9.125 -7.030 4.958 -1.822-3050.130 -5.986 -287.243 42.942 -12.990 8.535 -5.654 2.006-3329.361 14.781 -11.430 -275.497 37.982 -17.812 10.684 -3.608-4012.923 -8.975 8.751 -5.434 -286.390 49.157 -19.867 5.748-5073.524 5.086 -4.806 4.469 3.003 -312.263 65.370 -11.123-6394.193 -13.078 13.022 -14.378 17.381 -9.614 -319.061 68.044-7413.065 75.258 -74.995 83.354 -106.322 185.468 -235.855 -156.845-8826.008 exact solution u, computed us, error xg=-0.900, yg=-1.000, u= 2.991, us= 2.991err= 0.1240474E-10 xg=-0.900, yg=-0.900, u= 3.320, us= 3.320err= 0.1266320E-10 xg=-0.900, yg=-0.600, u= 3.995, us= 3.995err= -0.5097700E-11 xg=-0.900, yg=-0.200, u= 4.615, us= 4.615err= -0.2864375E-11 xg=-0.900, yg= 0.300, u= 6.020, us= 6.020err= 0.1104894E-11 xg=-0.900, yg= 0.800, u= 9.525, us= 9.525err= 0.3410605E-12 xg=-0.900, yg= 1.000, u=11.851, us= 11.851err= 0.6661338E-12 xg=-0.900, yg= 1.200, u=14.849, us= 14.849err= -0.2415845E-12 xg=-0.800, yg=-1.000, u= 3.968, us= 3.968err= 0.1789902E-10 xg=-0.800, yg=-0.900, u= 4.170, us= 4.170err= 0.2473133E-10 xg=-0.800, yg=-0.600, u= 4.512, us= 4.512err= 0.4145129E-11 xg=-0.800, yg=-0.200, u= 4.800, us= 4.800err= -0.1038813E-10 xg=-0.800, yg= 0.300, u= 5.970, us= 5.970err= 0.3073097E-11 xg=-0.800, yg= 0.800, u= 9.440, us= 9.440err= -0.4689582E-12 xg=-0.800, yg= 1.000, u=11.808, us= 11.808err= 0.5684342E-12 xg=-0.800, yg= 1.200, u=14.880, us= 14.880err= 0.7993606E-13 xg=-0.600, yg=-1.000, u= 5.904, us= 5.904err= 0.2374900E-10 xg=-0.600, yg=-0.900, u= 5.870, us= 5.870err= 0.3849365E-10 xg=-0.600, yg=-0.600, u= 5.600, us= 5.600err= 0.3620304E-10 xg=-0.600, yg=-0.200, u= 5.296, us= 5.296err= -0.5617729E-11 xg=-0.600, yg= 0.300, u= 6.086, us= 6.086err= -0.3584688E-11 xg=-0.600, yg= 0.800, u= 9.576, us= 9.576err= 0.9752199E-12 xg=-0.600, yg= 1.000, u=12.064, us= 12.064err= -0.3570477E-12 xg=-0.600, yg= 1.200, u=15.320, us= 15.320err= 0.2646772E-12 xg=-0.300, yg=-1.000, u= 8.853, us= 8.853err= 0.2834000E-10 xg=-0.300, yg=-0.900, u= 8.510, us= 8.510err= 0.5038281E-10 xg=-0.300, yg=-0.600, u= 7.457, us= 7.457err= 0.6750245E-10 xg=-0.300, yg=-0.200, u= 6.445, us= 6.445err= 0.3246914E-10 xg=-0.300, yg= 0.300, u= 6.890, us= 6.890err= -0.6022738E-11 xg=-0.300, yg= 0.800, u=10.635, us= 10.635err= -0.1900702E-12 xg=-0.300, yg= 1.000, u=13.393, us= 13.393err= 0.9912071E-12 xg=-0.300, yg= 1.200, u=17.015, us= 17.015err= -0.3907985E-13 xg= 0.000, yg=-1.000, u=12.000, us= 12.000err= 0.1589129E-10 xg= 0.000, yg=-0.900, u=11.402, us= 11.402err= 0.3652723E-10 xg= 0.000, yg=-0.600, u= 9.728, us= 9.728err= 0.8052581E-10 xg= 0.000, yg=-0.200, u= 8.224, us= 8.224err= 0.6071943E-10 xg= 0.000, yg= 0.300, u= 8.594, us= 8.594err= 0.1304912E-10 xg= 0.000, yg= 0.800, u=12.864, us= 12.864err= -0.3430145E-11 xg= 0.000, yg= 1.000, u=16.000, us= 16.000err= -0.1445954E-11 xg= 0.000, yg= 1.200, u=20.096, us= 20.096err= 0.2131628E-12 xg= 0.350, yg=-1.000, u=16.138, us= 16.138err= -0.4519052E-11 xg= 0.350, yg=-0.900, u=15.311, us= 15.311err= -0.1847411E-11 xg= 0.350, yg=-0.600, u=13.117, us= 13.117err= 0.3686118E-10 xg= 0.350, yg=-0.200, u=11.312, us= 11.312err= 0.7156054E-10 xg= 0.350, yg= 0.300, u=11.936, us= 11.936err= 0.3092993E-10 xg= 0.350, yg= 0.800, u=17.159, us= 17.159err= 0.4330758E-11 xg= 0.350, yg= 1.000, u=20.873, us= 20.873err= 0.2202682E-12 xg= 0.350, yg= 1.200, u=25.658, us= 25.658err= -0.5577760E-12 xg= 0.650, yg=-1.000, u=20.270, us= 20.270err= -0.8476775E-11 xg= 0.650, yg=-0.900, u=19.304, us= 19.304err= -0.1582734E-10 xg= 0.650, yg=-0.600, u=16.841, us= 16.841err= -0.1123013E-10 xg= 0.650, yg=-0.200, u=15.012, us= 15.012err= 0.3569411E-10 xg= 0.650, yg= 0.300, u=16.145, us= 16.145err= 0.4090950E-10 xg= 0.650, yg= 0.800, u=22.479, us= 22.479err= 0.7755574E-11 xg= 0.650, yg= 1.000, u=26.805, us= 26.805err= 0.3410605E-11 xg= 0.650, yg= 1.200, u=32.298, us= 32.298err= 0.1080025E-11 xg= 0.850, yg=-1.000, u=23.409, us= 23.409err= 0.3552714E-14 xg= 0.850, yg=-0.900, u=22.382, us= 22.382err= -0.7357670E-11 xg= 0.850, yg=-0.600, u=19.828, us= 19.828err= -0.2458478E-10 xg= 0.850, yg=-0.200, u=18.103, us= 18.103err= 0.6064482E-11 xg= 0.850, yg= 0.300, u=19.727, us= 19.727err= 0.3305800E-10 xg= 0.850, yg= 0.800, u=26.951, us= 26.951err= 0.1181988E-10 xg= 0.850, yg= 1.000, u=31.744, us= 31.744err= 0.3112177E-11 xg= 0.850, yg= 1.200, u=37.770, us= 37.770err= 0.1058709E-11 xg= 1.000, yg=-1.000, u=26.000, us= 26.000err= 0.7908341E-11 xg= 1.000, yg=-0.900, u=24.942, us= 24.942err= 0.8036238E-11 xg= 1.000, yg=-0.600, u=22.368, us= 22.368err= -0.1997691E-10 xg= 1.000, yg=-0.200, u=20.784, us= 20.784err= -0.1103473E-10 xg= 1.000, yg= 0.300, u=22.854, us= 22.854err= 0.2264855E-10 xg= 1.000, yg= 0.800, u=30.824, us= 30.824err= 0.1470823E-10 xg= 1.000, yg= 1.000, u=36.000, us= 36.000err= 0.5989875E-11 xg= 1.000, yg= 1.200, u=42.456, us= 42.456err= -0.8668621E-12 error= 0.10571624E-08 avg= 0.14682811E-10 max= 0.80525808E-10