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An efficient high‐order algorithm for solving systems of reaction‐diffusion equations
Author(s) -
Liao Wenyuan,
Zhu Jianping,
Khaliq Abdul Q.M.
Publication year - 2002
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/num.10012
Subject(s) - stencil , extrapolation , mathematics , reaction–diffusion system , richardson extrapolation , algorithm , partial differential equation , point (geometry) , crank–nicolson method , order (exchange) , nonlinear system , finite difference , diffusion , finite difference method , mathematical analysis , geometry , computational science , physics , finance , quantum mechanics , economics , thermodynamics
An efficient higher‐order finite difference algorithm is presented in this article for solving systems of two‐dimensional reaction‐diffusion equations with nonlinear reaction terms. The method is fourth‐order accurate in both the temporal and spatial dimensions. It requires only a regular five‐point difference stencil similar to that used in the standard second‐order algorithm, such as the Crank‐Nicolson algorithm. The Padé approximation and Richardson extrapolation are used to achieve high‐order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 340–354, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10012