A LINEAR SCHEME TO APPROXIMATE NONLINEAR CROSS-DIFFUSION SYSTEMS

作者：Murakawa Hideki^*

来源：Esaim: Mathematical Modelling and Numerical Analysis , 2011, 45(6): 1141-1161.

DOI：10.1051/m2an/2011010

• Cross-diffusion systems
• nonlinear diffusion
• discrete-time schemes
• numerical schemes
• Reaction-diffusion system approximations

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.

• 出版日期2011-12