28-Jul-2021 02:56:29 fem1d_heat_implicit_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test fem1d_heat_implicit(). fem1d_heat_implicit_test01(): Using the finite element method, compute an approximate solution to the time-dependent one dimensional heat equation. dH/dt - K * d2H/dx2 = f(x,t) Number of X nodes = 21 X interval = [ 0.000000, 1.000000 ] X step size = 0.050000 Number of T steps = 201 T interval = [ 0.000000, 80.000000 ] T step size = 0.400000 Number of elements = 20 Number of quadrature points = 3 H(X,T) written to "h_test01.txt" T values written to "t_test01.txt" X values written to "x_test01.txt" FEM1D_HEAT_IMPLICIT_TEST02: Using the finite element method, 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 = f(x,t) Number of X nodes = 21 X interval is [0.000000,1.000000] X step size = 0.050000 Number of T steps = 51 T interval is [0.000000,10.000000] T stepsize is 0.200000 Number of elements = 20 Number of quadrature points = 3 Step Time RMS Error 1 0 0 2 0.2 0.00439962 3 0.4 0.00800633 4 0.6 0.0109639 5 0.8 0.0133901 6 1 0.0153813 7 1.2 0.0170164 8 1.4 0.01836 9 1.6 0.0194651 10 1.8 0.0203749 11 2 0.0211249 12 2.2 0.0217442 13 2.4 0.0222565 14 2.6 0.0226813 15 2.8 0.0230346 16 3 0.0233294 17 3.2 0.0235764 18 3.4 0.0237844 19 3.6 0.0239605 20 3.8 0.0241106 21 4 0.0242395 22 4.2 0.0243511 23 4.4 0.0244488 24 4.6 0.0245351 25 4.8 0.0246122 26 5 0.024682 27 5.2 0.0247457 28 5.4 0.0248048 29 5.6 0.02486 30 5.8 0.0249124 31 6 0.0249624 32 6.2 0.0250107 33 6.4 0.0250578 34 6.6 0.025104 35 6.8 0.0251495 36 7 0.0251948 37 7.2 0.02524 38 7.4 0.0252852 39 7.6 0.0253307 40 7.8 0.0253766 41 8 0.0254229 42 8.2 0.0254699 43 8.4 0.0255175 44 8.6 0.0255658 45 8.8 0.025615 46 9 0.0256651 47 9.2 0.0257161 48 9.4 0.0257681 49 9.6 0.0258212 50 9.8 0.0258754 51 10 0.0259307 G(X,T) written to "g_test02.txt" H(X,T) written to "h_test02.txt" T values written to "t_test02.txt" X values written to "x_test02.txt" FEM1D_HEAT_IMPLICIT_TEST03: Using the finite element method, compute an approximate solution to the time-dependent one dimensional heat equation: dH/dt - K * d2H/dx2 = f(x,t) Number of X nodes = 21 X interval is [-5.000000,5.000000] X step size = 0.500000 Number of T steps = 81 T interval is [0.000000,4.000000] T stepsize is 0.050000 Number of elements = 20 Number of quadrature points = 3 H(X,T) written to "h_test03.txt" T values written to "t_test03.txt" X values written to "x_test3.txt" fem1d_heat_implicit_test(): Normal end of execution. 28-Jul-2021 02:56:34