07-Jan-2022 19:59:21

fem1d_heat_implicit_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  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.

07-Jan-2022 19:59:26