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A positive splitting method for mixed hyperbolic‐parabolic systems
Author(s) -
Gerisch Alf,
Griffiths David F.,
Weiner Rüdiger,
Chaplain Mark A. J.
Publication year - 2001
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/1098-2426(200103)17:2<152::aid-num5>3.0.co;2-a
Subject(s) - mathematics , hyperbolic partial differential equation , partial differential equation , discretization , method of lines , method of characteristics , mathematical analysis , ftcs scheme , parabolic partial differential equation , partial derivative , ordinary differential equation , elliptic partial differential equation , differential equation , differential algebraic equation
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. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 152–168, 2001