[soes]

Hello everybody,

I am using finite difference to solve linear internal wave 2d equations. I discretize the equation but at the end the linear system of equations do not come to a well format to be able to code it and solve it.

[FMDenaro]

Sorry, but it is very hard to read from your pages what you did...

It seems a second order PDE, is it hyperbolic? You can then reduce to a system of two equations of first order and solve with classical methods you can find in many textbook.
For example http://www.cambridge.org/se/academic...on-2nd-edition

[soes]

Originally Posted by FMDenaro

Sorry, but it is very hard to read from your pages what you did...

It seems a second order PDE, is it hyperbolic? You can then reduce to a system of two equations of first order and solve with classical methods you can find in many textbook.
For example http://www.cambridge.org/se/academic...on-2nd-edition

Thank you so much for the reply. I changed the pictures. In the typed picture you see how I discretize the equation. And on the written picture I considered a simple domain to see how equations look like. But if you look at the equations, although they are linear there is no systematic way to solve them, and this is my question how to solve them.
Thanks in advance

[FMDenaro]

but Wxx and Wzz are second derivatives in space? Therefore, you wrote a fourth-order PDE ....

I suggest to decompose in a lower order system of equations to analyse the nature of the PDE. Then you can simply apply any of the method in the book I linked.

[soes]

Originally Posted by FMDenaro

but Wxx and Wzz are second derivatives in space? Therefore, you wrote a fourth-order PDE ....

I suggest to decompose in a lower order system of equations to analyse the nature of the PDE. Then you can simply apply any of the method in the book I linked.

Thank you for the reply. It is basically simplified linear equation of internal waves
Yes they are spatial derivatives which go into time derivative (i.e. laplacian of time and space both).
But what do you mean exactly by decompose to lower order system?
Is my discretization wrong? I cannot proceed with discretization of the equation without modifying it?

[duri]

The LHS in the final equation has Wxx. I think it is typographical error, it should be W. Then the given equation is correct. By the way, what equation is this?. It looks very complicated.

[soes]

No it is unfortunately correct