I am solving a PDE using Mathematica. and I would like to know how to implement the condition that the three-variable function u[t, x, z]

A = 1.08152;  

B = 1.26415;

Cc = 431.188;

W = 0.0590505;

Phi = 1.590; 

eq = 
  {D[u[t, x, z], t] + A (u[t, x, z] D[u[t, x, z], z]) + B D[u[t, x, z], {z, 3}] + 
    B Cc D[D[u[t, x, z], {x, 2}], {z, 1}] == 0};

where u[0, x, z] = Phi (Sec[x/W])^2

I want to solve the PDE shown with NDSolve or NDSolveValue and plot its 3D graph.

  • $\begingroup$ Have you tried looking through the documentation? Try reference.wolfram.com/language/howto/… $\endgroup$ – ccosm Jul 4 '19 at 14:22
  • $\begingroup$ @ZahidKumai Do you mean initial conditions u[0,x,z]== Phi*(Sec[x/W])^2? $\endgroup$ – Alex Trounev Jul 4 '19 at 15:05
  • $\begingroup$ Yes, its use in initial condition. $\endgroup$ – Zahid Kumail Jul 4 '19 at 16:04
  • $\begingroup$ @ZahidKumail There were incorrect brackets with D[]. I edited, but not sure what is correct. Can you publish the equation in TeX form or give a link to the article where it is published? $\endgroup$ – Alex Trounev Jul 5 '19 at 5:39

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