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Thread: Confusion with Taylor Series

  1. #1
    Nov 2008

    Confusion with Taylor Series


    This technique of solving PDEs uses the Taylor expansion: link.

    To calculate $\displaystyle f$ at the $\displaystyle n+1^{th}$ time step, one needs to know $\displaystyle f$ at the $\displaystyle j+1^{th}$ distance step. But how is one expected to know the latter, since the unknown solution is a function of both time and distance?!

    Seeking clarification. Thanks.
    Last edited by algorithm; Oct 19th 2012 at 12:24 PM.
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  2. #2
    MHF Contributor
    Sep 2012

    Re: Confusion with Taylor Series

    Hey algorithm.

    Your series expansion for a two dimension function will look like f(x+a,y+a) = f(a,b) + df/dx|x=a*(x-a) + df/dy|y=b(y-b) + d^2f/dx^2*(x-a)^2 + d^2f/dxdy|x=a,y=b * (x-a)*(y-b) + ... +

    You can get an idea from here:

    Taylor series - Wikipedia, the free encyclopedia
    Thanks from algorithm
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