pde22_eq.f90 running differential equation to solve d^2u/dx^2 + d^2u/dy^2 = c(x,y) Uxx(X,Y) := 2^16 * 12*X^2 * (1-X)^4 * Y^4 * (1-Y)^4 - 32*X^3 * (1-X)^3 * Y^4 * (1-Y)^4 + 12*X^4 * (1-X)^2 * Y^4 * (1-Y)^4 Uyy(X,Y) := 2^16 * 12*X^4 * (1-X)^4 * Y^2 * (1-Y)^4 - 32*X^4 * (1-X)^4 * Y^3 * (1-Y)^3 + 12*X^4 * (1-X)^4 * Y^4 * (1-Y)^2 c(x,y) := Uxx(x,y) + Uyy(x,y) uniform grid on rectangle 0.0,1.0 to 0.0,1.0 known solution to test method u(x,y) = 2^16 * x^4 *(1-x)^4 * y^4 * (1-y)^4 xmin= 0.00000000000000 xmax= 1.00000000000000 nx= 10 ymin= 0.00000000000000 ymax= 1.00000000000000 ny= 10 start at 1423653.41200000 seconds xg( 1 )= 0.00000000000000 xg( 2 )= 0.111111111111111 xg( 3 )= 0.222222222222222 xg( 4 )= 0.333333333333333 xg( 5 )= 0.444444444444444 xg( 6 )= 0.555555555555556 xg( 7 )= 0.666666666666667 xg( 8 )= 0.777777777777778 xg( 9 )= 0.888888888888889 xg( 10 )= 1.00000000000000 yg( 1 )= 0.00000000000000 yg( 2 )= 0.111111111111111 yg( 3 )= 0.222222222222222 yg( 4 )= 0.333333333333333 yg( 5 )= 0.444444444444444 yg( 6 )= 0.555555555555556 yg( 7 )= 0.666666666666667 yg( 8 )= 0.777777777777778 yg( 9 )= 0.888888888888889 yg( 10 )= 1.00000000000000 u(0.5,0.5)= 1.00000000000000 c(0.5,0.5)= -64.0000000000000 internal cells zeroed matrix initialized solving took 0.014 seconds check_soln against PDE check soln against PDE max error= 4.180322754621102E-012 exact solution u, computed us, error xg= 0.111, yg= 0.111, u= 0.001, us= 0.001, err= -0.5106944E-12 xg= 0.111, yg= 0.222, u= 0.006, us= 0.006, err= -0.1633975E-11 xg= 0.111, yg= 0.333, u= 0.015, us= 0.015, err= -0.2405669E-11 xg= 0.111, yg= 0.444, u= 0.023, us= 0.023, err= -0.3521732E-11 xg= 0.111, yg= 0.556, u= 0.023, us= 0.023, err= -0.5662089E-11 xg= 0.111, yg= 0.667, u= 0.015, us= 0.015, err= -0.8467182E-11 xg= 0.111, yg= 0.778, u= 0.006, us= 0.006, err= -0.1024724E-10 xg= 0.111, yg= 0.889, u= 0.001, us= 0.001, err= -0.9055448E-11 xg= 0.222, yg= 0.111, u= 0.006, us= 0.006, err= -0.1624543E-11 xg= 0.222, yg= 0.222, u= 0.052, us= 0.052, err= -0.6755228E-11 xg= 0.222, yg= 0.333, u= 0.143, us= 0.143, err= -0.1179384E-10 xg= 0.222, yg= 0.444, u= 0.217, us= 0.217, err= -0.1668055E-10 xg= 0.222, yg= 0.556, u= 0.217, us= 0.217, err= -0.2123954E-10 xg= 0.222, yg= 0.667, u= 0.143, us= 0.143, err= -0.2499714E-10 xg= 0.222, yg= 0.778, u= 0.052, us= 0.052, err= -0.2623781E-10 xg= 0.222, yg= 0.889, u= 0.006, us= 0.006, err= -0.2380085E-10 xg= 0.333, yg= 0.111, u= 0.015, us= 0.015, err= -0.2394317E-11 xg= 0.333, yg= 0.222, u= 0.143, us= 0.143, err= -0.1178918E-10 xg= 0.333, yg= 0.333, u= 0.390, us= 0.390, err= -0.2074130E-10 xg= 0.333, yg= 0.444, u= 0.594, us= 0.594, err= -0.2898670E-10 xg= 0.333, yg= 0.556, u= 0.594, us= 0.594, err= -0.3593537E-10 xg= 0.333, yg= 0.667, u= 0.390, us= 0.390, err= -0.4125966E-10 xg= 0.333, yg= 0.778, u= 0.143, us= 0.143, err= -0.4297845E-10 xg= 0.333, yg= 0.889, u= 0.015, us= 0.015, err= -0.4184600E-10 xg= 0.444, yg= 0.111, u= 0.023, us= 0.023, err= -0.3508877E-11 xg= 0.444, yg= 0.222, u= 0.217, us= 0.217, err= -0.1667005E-10 xg= 0.444, yg= 0.333, u= 0.594, us= 0.594, err= -0.2898137E-10 xg= 0.444, yg= 0.444, u= 0.905, us= 0.905, err= -0.3989775E-10 xg= 0.444, yg= 0.556, u= 0.905, us= 0.905, err= -0.4840184E-10 xg= 0.444, yg= 0.667, u= 0.594, us= 0.594, err= -0.5435663E-10 xg= 0.444, yg= 0.778, u= 0.217, us= 0.217, err= -0.5584025E-10 xg= 0.444, yg= 0.889, u= 0.023, us= 0.023, err= -0.5560177E-10 xg= 0.556, yg= 0.111, u= 0.023, us= 0.023, err= -0.5646605E-11 xg= 0.556, yg= 0.222, u= 0.217, us= 0.217, err= -0.2122735E-10 xg= 0.556, yg= 0.333, u= 0.594, us= 0.594, err= -0.3592870E-10 xg= 0.556, yg= 0.444, u= 0.905, us= 0.905, err= -0.4839895E-10 xg= 0.556, yg= 0.556, u= 0.905, us= 0.905, err= -0.5690148E-10 xg= 0.556, yg= 0.667, u= 0.594, us= 0.594, err= -0.6130019E-10 xg= 0.556, yg= 0.778, u= 0.217, us= 0.217, err= -0.6039100E-10 xg= 0.556, yg= 0.889, u= 0.023, us= 0.023, err= -0.5773298E-10 xg= 0.667, yg= 0.111, u= 0.015, us= 0.015, err= -0.8446306E-11 xg= 0.667, yg= 0.222, u= 0.143, us= 0.143, err= -0.2498032E-10 xg= 0.667, yg= 0.333, u= 0.390, us= 0.390, err= -0.4124967E-10 xg= 0.667, yg= 0.444, u= 0.594, us= 0.594, err= -0.5435108E-10 xg= 0.667, yg= 0.556, u= 0.594, us= 0.594, err= -0.6129697E-10 xg= 0.667, yg= 0.667, u= 0.390, us= 0.390, err= -0.6175543E-10 xg= 0.667, yg= 0.778, u= 0.143, us= 0.143, err= -0.5614892E-10 xg= 0.667, yg= 0.889, u= 0.015, us= 0.015, err= -0.4786618E-10 xg= 0.778, yg= 0.111, u= 0.006, us= 0.006, err= -0.1022614E-10 xg= 0.778, yg= 0.222, u= 0.052, us= 0.052, err= -0.2621877E-10 xg= 0.778, yg= 0.333, u= 0.143, us= 0.143, err= -0.4296635E-10 xg= 0.778, yg= 0.444, u= 0.217, us= 0.217, err= -0.5583142E-10 xg= 0.778, yg= 0.556, u= 0.217, us= 0.217, err= -0.6038453E-10 xg= 0.778, yg= 0.667, u= 0.143, us= 0.143, err= -0.5614528E-10 xg= 0.778, yg= 0.778, u= 0.052, us= 0.052, err= -0.4566273E-10 xg= 0.778, yg= 0.889, u= 0.006, us= 0.006, err= -0.3234503E-10 xg= 0.889, yg= 0.111, u= 0.001, us= 0.001, err= -0.9015642E-11 xg= 0.889, yg= 0.222, u= 0.006, us= 0.006, err= -0.2378189E-10 xg= 0.889, yg= 0.333, u= 0.015, us= 0.015, err= -0.4183225E-10 xg= 0.889, yg= 0.444, u= 0.023, us= 0.023, err= -0.5559296E-10 xg= 0.889, yg= 0.556, u= 0.023, us= 0.023, err= -0.5772196E-10 xg= 0.889, yg= 0.667, u= 0.015, us= 0.015, err= -0.4785656E-10 xg= 0.889, yg= 0.778, u= 0.006, us= 0.006, err= -0.3234267E-10 xg= 0.889, yg= 0.889, u= 0.001, us= 0.001, err= -0.1744022E-10 avgerr= 0.31606400E-10 maxerr= 0.61755434E-10 writing pde22_eq_f90.dat finished writing pde22_eq_f90.dat pde22_eq.f90 finished in 0.055 seconds