[Schrödinger's hat]

Couldn't quite figure out whether to put this in Physics, Calculus, Applied Mathematics, Computer Science, or Engineering :/

I'm trying to come up with a good scheme for integrating something similar to a thin beam equation:
Something along the lines of:


But unfortunately comp-phys is but a hazy memory.

I can remember/find notes on enough to do similar things which are first order in time with finite difference methods.
Would the obvious thing of adding degrees of freedom to make:



Then applying the same methods be an effective approach? Or would it be horribly unstable?
Is there an out-of-the-box method somewhere that I'm completely missing?

This post has been edited by Schrödinger's hat: 30 September 2011 - 12:41 PM

[Schrödinger's hat]

Schrödinger, on 30 September 2011 - 12:30 PM, said:

Then applying the same methods be an effective approach? Or would it be horribly unstable?

In case anyone else cares/comes here looking for an answer to the same question, this seems to work quite well.
The resulting system was horribly unstable with Euler method, but anything backwards-time or mixed seemed to work remarkably well.

I suppose I won't know for sure until it's compared to some data.

If anyone is watching/curious I can elaborate upon request, as there seems to be a bit of a jump in the learning curve (for what I can find online at least).

[khaled]

Take a look at these references:

Solution using separation of variables

Wilmott

PDE Integration with Physics Model

Scientific Notes on PDEs

PDE Integration using Discretization

Wolfram Notes on Numerical Solutions to PDE

PDE as a Linear System

PDE and Relaxation Methods

.. good luck,