How to solve PDE problem

Hi

i solved one of my PDE problems with solve single pde document but i can't use this format for problems like

can i use pdepe to solve it

please help me to solve this problem

thank you

Answer 1

[Bill Greene]

Your PDE can replaced by these two PDE

which is a form acceptable to pdepe. However, pdepe, or in fact

any numerical method, will run into problems because at your

boundary conditions and initial conditions are inconsistent. Mathematically

this is referred to as an ill-posed problem and consequently has no solution.

[jesse]

thank you very much

it's a big help

Answer 2

[John D'Errico]

This is second order in the time derivative, so there is a utt term. But that should make in not in the realm of pdepe, which allows only ut terms.

Personally, I would just approximate the derivatives using second order finite differences. Convert the entire problem to that of solving a linear system of equations. Given a discretization with nt nodes in t and nx nodes in x, system will be nt*nx by nt*nx. Using sparse to formulate the problem, it will be solvable, though hyperbolic. And that means it may be poorly conditioned, so I would be looking carefully at the singular values and the condition number.

As I said, easily writable. Why not try it? I ask this, because I've never seen a problem as simply stated that was not homework. And if this is homework, I won't do homework. I will help, if you make a credible effort. If you come close enough, I might even show what I would try.

[jesse]

thank you for your reply.

as you guess it's a homework.

according to your reply i will convert it to a linear system and try to solve it.

thank you again