A positive splitting method for mixed hyperbolic-parabolic systems

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

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2001


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


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