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Math Help - Solving PDEs

  1. #1
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    Solving PDEs

    Hi,

    Given a PDE of this form



    then one way to solve it iteratively is



    (Equations from IISc).

    The update equation has me confused for the following reason. u(x, t) appears in the PDE as function of both time t and distance x. However, the update equation only gives you u as a function of time ( u^{n+1}_{j}), and what's more, it seems to assume that u is already known as a function of distance because it has u^{n}_{j+1} terms.

    In short, the solver seems to assume that you already know the solution .

    Anyone familiar with this who can enlighten me?

    Thanks.
    Last edited by algorithm; October 20th 2012 at 04:09 AM.
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  2. #2
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    Re: Solving PDEs

    Hey algorithm.

    What is the definition of u_j given in your book?
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  3. #3
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    Re: Solving PDEs

    chiro,

    Thanks for your reply.

    u^n_{j} is defined as the numerical approximation of u(x, t) at time index n, and distance index x. So basically it represents the n^{th} time iteration and the j^{th} distance iteration of the solver algorithm.
    Last edited by algorithm; October 21st 2012 at 06:24 AM.
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  4. #4
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    Re: Solving PDEs

    What is the taylor series expansion look like and how similar is it to your approximation (where dx's, dt's, etc are approximated by delta_x, delta_t etc)?
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