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A linear scheme to approximate nonlinear cross-diffusion systems*

Published online by Cambridge University Press:  04 July 2011

Hideki Murakawa
Hideki Murakawa*
Affiliation:
Faculty of Mathematics, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819-0395 Japan. murakawa@math.kyushu-u.ac.jp
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Abstract

This paper proposes a linear discrete-time scheme for general nonlinear cross-diffusion systems. The scheme can be regarded as an extension of a linear scheme based on the nonlinear Chernoff formula for the degenerate parabolic equations, which proposed by Berger et al. [RAIRO Anal. Numer. 13 (1979) 297–312]. We analyze stability and convergence of the linear scheme. To this end, we apply the theory of reaction-diffusion system approximation. After discretizing the scheme in space, we obtain a versatile, easy to implement and efficient numerical scheme for the cross-diffusion systems. Numerical experiments are carried out to demonstrate the effectiveness of the proposed scheme.

Keywords

Cross-diffusion systemsnonlinear diffusiondiscrete-time schemesnumerical schemesReaction-diffusion system approximations
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 6 , November 2011 , pp. 1141 - 1161
Copyright
© EDP Sciences, SMAI, 2011

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