Advanced Studies in Pure Mathematics

Numerical solution of nonlinear cross-diffusion systems by a linear scheme

Hideki Murakawa

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This paper introduces a linear scheme to approximate the solutions of the general nonlinear cross-diffusion system. After discretizing the scheme in space, we obtain a versatile, easy to implement and stable numerical scheme for the cross-diffusion system. Numerical experiments are carried out to examine rates of convergence with respect to the time step and the spatial mesh sizes.

Article information

Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 243-251

Received: 20 April 2012
Revised: 29 January 2013
First available in Project Euclid: 30 October 2018

Permanent link to this document euclid.aspm/1540934220

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations 35K57: Reaction-diffusion equations 65M12: Stability and convergence of numerical methods 92D25: Population dynamics (general)

Cross-diffusion systems nonlinear diffusion discrete-time schemes numerical schemes


Murakawa, Hideki. Numerical solution of nonlinear cross-diffusion systems by a linear scheme. Nonlinear Dynamics in Partial Differential Equations, 243--251, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410243.

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