Sat Apr 12 09:29:50 2025

traveling_wave_exact_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test traveling_wave_exact(),
  an exact traveling wave solution of the wave equation.

  parameters:
    a     =  2.0
    k     =  6.0
    w     =  1.0
    phi   =  0.7853981633974483
    xmin  =  -1.0
    xmax  =  1.0
    t0    =  0.0
    tstop =  5.0

traveling_wave_residual_test():
  Evaluate solution and residual at selected points (X,T)

      X       T       U(X,T)      Resid(X,T)

   -1.0000    0.0000       1.753  -2.22045e-16
   -0.8000    0.0000       1.533  0
   -0.6000    0.0000     -0.6424  0
   -0.4000    0.0000      -1.998  0
   -0.2000    0.0000     -0.8057  1.11022e-16
    0.0000    0.0000       1.414  0
    0.2000    0.0000       1.831  -2.22045e-16
    0.4000    0.0000    -0.08758  1.38778e-17
    0.6000    0.0000      -1.894  2.22045e-16
    0.8000    0.0000      -1.285  0
    1.0000    0.0000      0.9627  0

   -1.0000    1.2500       1.466  0
   -0.8000    1.2500     -0.7362  0
   -0.6000    1.2500          -2  0
   -0.4000    1.2500     -0.7132  0
   -0.2000    1.2500       1.483  0
    0.0000    1.2500       1.788  -2.22045e-16
    0.2000    1.2500     -0.1873  0
    0.4000    1.2500      -1.924  0
    0.6000    1.2500      -1.207  0
    0.8000    1.2500       1.049  0
    1.0000    1.2500       1.967  0

   -1.0000    2.5000     -0.8283  1.11022e-16
   -0.8000    2.5000      -1.997  0
   -0.6000    2.5000     -0.6189  0
   -0.4000    2.5000       1.548  0
   -0.2000    2.5000       1.741  0
    0.0000    2.5000     -0.2866  0
    0.2000    2.5000      -1.949  2.22045e-16
    0.4000    2.5000      -1.126  0
    0.6000    2.5000       1.133  0
    0.8000    2.5000       1.947  0
    1.0000    2.5000      0.2779  0

   -1.0000    3.7500      -1.989  2.22045e-16
   -0.8000    3.7500      -0.523  0
   -0.6000    3.7500        1.61  0
   -0.4000    3.7500        1.69  0
   -0.2000    3.7500     -0.3852  5.55112e-17
    0.0000    3.7500      -1.969  2.22045e-16
    0.2000    3.7500      -1.042  0
    0.4000    3.7500       1.214  0
    0.6000    3.7500       1.921  -2.22045e-16
    0.8000    3.7500      0.1785  0
    1.0000    3.7500      -1.792  0

   -1.0000    5.0000     -0.4259  0
   -0.8000    5.0000       1.667  -2.22045e-16
   -0.6000    5.0000       1.634  0
   -0.4000    5.0000     -0.4828  0
   -0.2000    5.0000      -1.984  0
    0.0000    5.0000      -0.955  1.11022e-16
    0.2000    5.0000       1.292  0
    0.4000    5.0000       1.891  0
    0.6000    5.0000     0.07874  0
    0.8000    5.0000      -1.834  0
    1.0000    5.0000      -1.408  0


traveling_wave_plot():
  Plot the traveling wave over several time steps
  Graphics saved as "traveling_wave_exact.png"

traveling_wave_exact_test():
  Normal end of execution.
Sat Apr 12 09:29:51 2025