Re: Can I solve that with Runge-Kutta?

From: Donald R. Fredkin (drfredkin_at_sbcglobal.net)
Date: 03/09/05

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    Date: Wed, 09 Mar 2005 06:54:30 GMT

    "J DUDLEY" <sbdpumbaa@blueyonder.co.uk> wrote in
    news:x1oXd.19219$y25.6413@fe3.news.blueyonder.co.uk:

    > What is in the Langevin equation that inhibits a Runge-Kutta code?
    > Typically all I have found that prevents 'success' is stiffness, with
    > stiffness increasing (approximately) as the square of the number of
    > elements.

    The Langevin equation is a stochastic differential equation (SDE). None of
    the standard techniques for solution of ordinary differential equations are
    applicable. You must, to start, understand what it means to solve an
    equation containing terms which are given only in a statistical sense. And
    then you must recognize the extreme lack of smoothness in the random terms.
    Stiffness is not an issue, and the BDF methods appropriate to stiff
    equations are guaranteed to fail for SDEs.

    There is an extensive literature on the subject. A reasonably undemanding
    starting point might be "Numerical solution of stochastic differential
    equations" by Peter E. Kloeden and Eckhard Platen, Springer-Verlag, 1992.

    I do not know of any canned codes.

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