28-Jul-2021 02:29:03 fd1d_heat_implicit_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test fd1d_heat_implicit() test01: Compute an approximate solution to the time-dependent one dimensional heat equation: dH/dt - K * d2H/dx2 = 0 Constant K = 3 Number of X nodes = 21 X interval is [-5.000000,5.000000] X spacing is 0.500000 Number of T values = 81 T interval is [0.000000,4.000000] T spacing is 0.050000 CFL coefficient = 0.6 Graphics saved as "test01.png" test02: Compute an approximate solution to the time-dependent one dimensional heat equation for a problem where we know the exact solution. dH/dt - K * d2H/dx2 = 0 Constant K = 2 Number of X nodes = 21 X interval is [-5.000000,5.000000] X spacing is 0.500000 Number of T values = 81 T interval is [0.000000,1.000000] T spacing is 0.012500 CFL coefficient = 0.1 Step Time RMS Error 1 0 0 2 0.0125 0.0218923 3 0.025 0.0425743 4 0.0375 0.062135 5 0.05 0.0806518 6 0.0625 0.0981927 7 0.075 0.114818 8 0.0875 0.130582 9 0.1 0.145535 10 0.1125 0.159721 11 0.125 0.173182 12 0.1375 0.185955 13 0.15 0.198078 14 0.1625 0.209582 15 0.175 0.220499 16 0.1875 0.230859 17 0.2 0.240687 18 0.2125 0.250011 19 0.225 0.258853 20 0.2375 0.267239 21 0.25 0.275188 22 0.2625 0.282721 23 0.275 0.289859 24 0.2875 0.29662 25 0.3 0.303021 26 0.3125 0.309079 27 0.325 0.31481 28 0.3375 0.32023 29 0.35 0.325352 30 0.3625 0.330192 31 0.375 0.334761 32 0.3875 0.339073 33 0.4 0.34314 34 0.4125 0.346973 35 0.425 0.350583 36 0.4375 0.353982 37 0.45 0.357178 38 0.4625 0.360182 39 0.475 0.363002 40 0.4875 0.365649 41 0.5 0.368129 42 0.5125 0.370452 43 0.525 0.372625 44 0.5375 0.374655 45 0.55 0.376549 46 0.5625 0.378315 47 0.575 0.379959 48 0.5875 0.381487 49 0.6 0.382905 50 0.6125 0.384218 51 0.625 0.385433 52 0.6375 0.386555 53 0.65 0.387587 54 0.6625 0.388536 55 0.675 0.389406 56 0.6875 0.390201 57 0.7 0.390926 58 0.7125 0.391584 59 0.725 0.392179 60 0.7375 0.392715 61 0.75 0.393195 62 0.7625 0.393624 63 0.775 0.394003 64 0.7875 0.394337 65 0.8 0.394627 66 0.8125 0.394877 67 0.825 0.395089 68 0.8375 0.395267 69 0.85 0.395411 70 0.8625 0.395526 71 0.875 0.395612 72 0.8875 0.395672 73 0.9 0.395708 74 0.9125 0.395722 75 0.925 0.395715 76 0.9375 0.395689 77 0.95 0.395646 78 0.9625 0.395588 79 0.975 0.395516 80 0.9875 0.395431 81 1 0.395334 Graphics saved as "test02.png" test03: Compute an approximate solution to the time-dependent one dimensional heat equation: dH/dt - K * d2H/dx2 = 0 Constant K = 2 Number of X nodes = 21 X interval is [-5.000000,5.000000] X spacing is 0.500000 Number of T values = 81 T interval is [0.000000,2.000000] T spacing is 0.025000 CFL coefficient = 0.2 Graphics saved as "test03.png" fd1d_heat_implicit_test(): Normal end of execution. 28-Jul-2021 02:29:09