A linear scheme to approximate nonlinear cross-diffusion systems
Hideki Murakawa (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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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 [ (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...