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Numerical Methods for PDEs, basic algorithm?

  1. Jan 23, 2013 #1
    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. :cry: And I got so little time :cry: 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.
  2. jcsd
  3. Jan 25, 2013 #2
    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.
  4. Jan 25, 2013 #3
    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
    Last edited: Jan 25, 2013
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