Advanced Studies in Pure Mathematics

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

Hideki Murakawa

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934220

Digital Object Identifier
doi:10.2969/aspm/06410243

Mathematical Reviews number (MathSciNet)
MR3381209

Zentralblatt MATH identifier
1337.65117

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

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

Citation

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. https://projecteuclid.org/euclid.aspm/1540934220


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