1 October 2024 8:20:21.044 PM poisson_1d_test(): Fortran77 version Test poisson_1d(). test01(): poisson_1d() solves a 1D Poisson BVP using the Gauss-Seidel method. -u"(x) = 1, for 0 < x < 1 u(0) = u(1) = 0. Solution is u(x) = ( -x^2 + x ) / 2 Mesh index K = 5 Number of intervals N=2^K = 32 Number of nodes = 2^K+1 = 33 I X(I) U(I) U Exact(X(I)) 1 0.0000 0.00000 0.00000 2 0.0312 0.150838E-01 0.151367E-01 3 0.0625 0.291920E-01 0.292969E-01 4 0.0938 0.423251E-01 0.424805E-01 5 0.1250 0.544837E-01 0.546875E-01 6 0.1562 0.656682E-01 0.659180E-01 7 0.1875 0.758789E-01 0.761719E-01 8 0.2188 0.851163E-01 0.854492E-01 9 0.2500 0.933807E-01 0.937500E-01 10 0.2812 0.100672 0.101074 11 0.3125 0.106992 0.107422 12 0.3438 0.112339 0.112793 13 0.3750 0.116714 0.117188 14 0.4062 0.120118 0.120605 15 0.4375 0.122549 0.123047 16 0.4688 0.124009 0.124512 17 0.5000 0.124497 0.125000 18 0.5312 0.124014 0.124512 19 0.5625 0.122559 0.123047 20 0.5938 0.120131 0.120605 21 0.6250 0.116732 0.117188 22 0.6562 0.112360 0.112793 23 0.6875 0.107016 0.107422 24 0.7188 0.100699 0.101074 25 0.7500 0.934081E-01 0.937500E-01 26 0.7812 0.851440E-01 0.854492E-01 27 0.8125 0.759058E-01 0.761719E-01 28 0.8438 0.656933E-01 0.659180E-01 29 0.8750 0.545060E-01 0.546875E-01 30 0.9062 0.423435E-01 0.424805E-01 31 0.9375 0.292052E-01 0.292969E-01 32 0.9688 0.150909E-01 0.151367E-01 33 1.0000 0.00000 0.00000 Maximum error = 0.502527E-03 Number of Gauss-Seidel iterations = 575 test02() poisson_1d() solves a 1D Poisson BVP using the Gauss-Seidel method. -u"(x) = - x * (x+3) * exp(x), for 0 < x < 1 u(0) = u(1) = 0. Solution is u(x) = x * (x-1) * exp(x) Mesh index K = 5 Number of intervals N=2^K = 32 Number of nodes = 2^K+1 = 33 I X(I) U(I) U Exact(X(I)) 1 0.0000 0.00000 -0.00000 2 0.0312 -0.311615E-01 -0.312344E-01 3 0.0625 -0.622285E-01 -0.623727E-01 4 0.0938 -0.930982E-01 -0.933113E-01 5 0.1250 -0.123659 -0.123938 6 0.1562 -0.153789 -0.154132 7 0.1875 -0.183360 -0.183762 8 0.2188 -0.212230 -0.212687 9 0.2500 -0.240247 -0.240755 10 0.2812 -0.267250 -0.267803 11 0.3125 -0.293063 -0.293657 12 0.3438 -0.317498 -0.318127 13 0.3750 -0.340356 -0.341014 14 0.4062 -0.361420 -0.362101 15 0.4375 -0.380460 -0.381157 16 0.4688 -0.397230 -0.397938 17 0.5000 -0.411467 -0.412180 18 0.5312 -0.422892 -0.423603 19 0.5625 -0.431206 -0.431908 20 0.5938 -0.436089 -0.436777 21 0.6250 -0.437204 -0.437870 22 0.6562 -0.434189 -0.434828 23 0.6875 -0.426662 -0.427268 24 0.7188 -0.414214 -0.414782 25 0.7500 -0.396415 -0.396938 26 0.7812 -0.372803 -0.373277 27 0.8125 -0.342894 -0.343312 28 0.8438 -0.306169 -0.306528 29 0.8750 -0.262082 -0.262377 30 0.9062 -0.210054 -0.210280 31 0.9375 -0.149470 -0.149624 32 0.9688 -0.796810E-01 -0.797599E-01 33 1.0000 0.00000 0.00000 Maximum error = 0.712828E-03 Number of Gauss-Seidel iterations = 702 poisson_1d_test(): Normal end of execution. 1 October 2024 8:20:21.045 PM