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07-Oct-2025 21:39:05

helmholtz_exact_test():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Test helmholtz_exact().

  Helmholtz exact solution with
  m = 1, n = 2

  k   X(k)  Y(k)  Z(k)

   1      0.0000      0.0000              -0
   2      0.7500      0.0000          3.6405
   3      1.0607      0.0000         3.51926
   4      1.2990      0.0000         1.87913
   5      1.5000      0.0000     5.90971e-16
   6      0.2318      0.7133        -1.34035
   7      0.3278      1.0087        -1.29572
   8      0.4014      1.2355       -0.691853
   9      0.4635      1.4266    -1.95824e-15
  10     -0.6068      0.4408        -1.47176
  11     -0.8581      0.6234        -1.42275
  12     -1.0509      0.7636       -0.759684
  13     -1.2135      0.8817    -2.38915e-16
  14     -0.6068     -0.4408         3.72172
  15     -0.8581     -0.6234         3.59778
  16     -1.0509     -0.7636         1.92105
  17     -1.2135     -0.8817     6.04155e-16
  18      0.2318     -0.7133         -4.5501
  19      0.3278     -1.0087        -4.39857
  20      0.4014     -1.2355        -2.34864
  21      0.4635     -1.4266    -7.38629e-16
  Graphics saved as "helmholtz_exact_m1_n2.png"

  Helmholtz exact solution with
  m = 2, n = 3

  k   X(k)  Y(k)  Z(k)

   1      0.0000      0.0000               0
   2      0.7500      0.0000         3.07182
   3      1.0607      0.0000         -1.1543
   4      1.2990      0.0000          -2.142
   5      1.5000      0.0000     1.06448e-15
   6      0.2318      0.7133        -3.83934
   7      0.3278      1.0087         1.44271
   8      0.4014      1.2355         2.67719
   9      0.4635      1.4266     3.10439e-15
  10     -0.6068      0.4408         3.14035
  11     -0.8581      0.6234        -1.18005
  12     -1.0509      0.7636        -2.18979
  13     -1.2135      0.8817     1.08823e-15
  14     -0.6068     -0.4408        -1.24186
  15     -0.8581     -0.6234        0.466655
  16     -1.0509     -0.7636        0.865958
  17     -1.2135     -0.8817    -4.30345e-16
  18      0.2318     -0.7133        -1.13098
  19      0.3278     -1.0087        0.424988
  20      0.4014     -1.2355        0.788638
  21      0.4635     -1.4266     -3.9192e-16
  Graphics saved as "helmholtz_exact_m2_n3.png"

helmholtz_exact_test():
  Normal end of execution.

07-Oct-2025 21:39:15