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Math Help - Numerical Differentiation help needed.

  1. #1
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    Numerical Differentiation help needed.

    Hello,

    I have a bit of a problem that I was hoping someone might be able to help me with. I'll start by explaining what I am attempting to do and explain where I need help.

    I'm trying to program a simulation of the Viscous Burger's Equation in 1 dimension. I'm going to use an implicit finite difference scheme (Crank-Nicolson) to do this.

    The problem I have is the fact that the Burger's equation I mentioned is non-linear, I need to have this equation in conservation form before I apply my scheme. The Burgers equation in conservation form is as follows:

    dU/dt + dF/dx = vd^2U/dx^2 (note: I didn't know how to show these as partial derivatives. All derivatives are partial here.)
    Where F is a flux function F = U^2/2
    and v is the viscosity which is a constant.
    I was just wondering what is the best way of linearizing this equation? If you can show me or give me steps to follow so I can ask follow up questions that would be brilliant.

    Is it best to linearize this before or after applying the difference scheme? (which is nicer?)

    I want to thank you for any help you can give in advance.

    All the best,

    Wayne.
    Last edited by waynex; November 21st 2007 at 04:54 AM.
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