# Numerical solution of a PDE having boundary conditions

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.

• Have you tried looking through the documentation? Try reference.wolfram.com/language/howto/… – ccosm Jul 4 '19 at 14:22
• @ZahidKumai Do you mean initial conditions u[0,x,z]== Phi*(Sec[x/W])^2? – Alex Trounev Jul 4 '19 at 15:05
• Yes, its use in initial condition. – Zahid Kumail Jul 4 '19 at 16:04
• @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? – Alex Trounev Jul 5 '19 at 5:39