A linear scheme to approximate nonlinear cross-diffusion systems

Hideki Murakawa

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1141-1161
Number of pages21
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number6
Publication statusPublished - Nov 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics


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