Numerical Methods for PDEs, basic algorithm?


by maistral
Tags: algorithm, methods, numerical, pde, step
maistral
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#1
Jan23-13, 05:33 AM
P: 72
This is actually a request, I don't know if these are the correct forums for me to post these kinds of things, but yeah. Alright. I intended to study and learn numerical methods with PDEs on my own.

And sadly the only thing I can comprehend is the Liebmann method. And I got so little time our professor didn't have the luxury of time to discuss numerical methods for PDEs (but I fear that I may encounter these problems soon, and I don't want to be a sitting duck when that time comes).

So yeah, can I ask for at least a basic/step by step pseudo-algorithm for numerical techniques for PDEs? Because I read Kreyszig's and O'Neil's book and yeah, the only thing I can comprehend is the Liebmann method.
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Chestermiller
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#2
Jan25-13, 12:56 PM
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Quote Quote by maistral View Post
This is actually a request, I don't know if these are the correct forums for me to post these kinds of things, but yeah. Alright. I intended to study and learn numerical methods with PDEs on my own.

And sadly the only thing I can comprehend is the Liebmann method. And I got so little time our professor didn't have the luxury of time to discuss numerical methods for PDEs (but I fear that I may encounter these problems soon, and I don't want to be a sitting duck when that time comes).

So yeah, can I ask for at least a basic/step by step pseudo-algorithm for numerical techniques for PDEs? Because I read Kreyszig's and O'Neil's book and yeah, the only thing I can comprehend is the Liebmann method.
The type of numerical method you use depends on nature of the PDE you are solving: elliptic, parabolic, hyperbolic. Even within each of these categories, there are many different numerical techniques that are used.
Studiot
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#3
Jan25-13, 06:39 PM
P: 5,462
Gosh numerical solution of partial differential equations. self taught. That's a big subject indeed.



I assume you know some of the techniques for ordinary differential equations?
I hope you have the means to solve large sets of simultaneous algebraic (usually linear) equations.

You can rewrite the equation in terms of finite differences -crank nicholson, for instance still works.

You can set up a grid over the region of application and apply simplified functions. This is the basis of the finite element method.

You can use Greens / Stokes / Gauss theorems to relate the PDE within the region to functions on the boundary. This is the basis of the boundary element method.

Special methods such as the shooting method of work for a ball park solution, when nothing else does.

Since you have not found much in your existing texts here is a short bibliography of numeric PDEs

Finite Difference Equations : Levy & Lessman

Numerical Analysis : Kincaid & Cheney

Elementary Applied Partial Differential Equations : Haberman

A First Course in Partial Differential Equations : Weinberger

Elements of Computational Hydraulics : Koutitas

Numerical Methods for Partial Differential Equations : Ames

Numerical Solutions of Partial Differential Equations : Morton & Mayers

Several titles about Boundary Elements : Brebbia

Numerical Solution of Partial Differenctial Equations Finite Difference Methods : Smith

This last one is an excellent book for self teaching.

go well in your efforts


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