A linear scheme to approximate nonlinear cross-diffusion systems*
Faculty of Mathematics, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819-0395 Japan. email@example.com
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.
Mathematics Subject Classification: 35K55 / 35K57 / 65M12 / 92D25
Key words: Cross-diffusion systems / nonlinear diffusion / discrete-time schemes / numerical schemes / Reaction-diffusion system approximations
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