A positive splitting method for mixed hyperbolic-parabolic systems

Alf Gerisch, David F. Griffiths, Rudiger Weiner, Mark A. J. Chaplain

    Research output: Contribution to journalArticle

    30 Citations (Scopus)

    Abstract

    In this article we present a method of lines approach to the numerical solution of a system of coupled hyperbolic - parabolic partial differential equations (PDEs). Special attention is paid to preserving the positivity of the solution of the PDEs when this solution is approximated numerically. This is achieved by using a flux-limited spatial discretization for the hyperbolic equation. We use splitting techniques for the solution of the resulting large system of stiff ordinary differential equations. The performance of the approach applied to a biomathematical model is compared with the performance of standard methods.
    Original languageEnglish
    Pages (from-to)152-168
    Number of pages17
    JournalNumerical Methods for Partial Differential Equations
    Volume17
    Issue number2
    DOIs
    Publication statusPublished - 2001

    Keywords

    • Mixed hyperbolic-parabolic PDE system
    • Finite difference approximation
    • Method of lines
    • Splitting methods
    • Positive methods

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