A linear scheme to approximate nonlinear cross-diffusion systems*

Hideki Murakawa

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 6, page 1141-1161
  • ISSN: 0764-583X

Abstract

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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 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.

How to cite

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Murakawa, Hideki. "A linear scheme to approximate nonlinear cross-diffusion systems*." ESAIM: Mathematical Modelling and Numerical Analysis 45.6 (2011): 1141-1161. <http://eudml.org/doc/276354>.

@article{Murakawa2011,
abstract = { 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. },
author = {Murakawa, Hideki},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Cross-diffusion systems; nonlinear diffusion; discrete-time schemes; numerical schemes; Reaction-diffusion system approximations; cross-diffusion systems; reaction-diffusion system; stability; convergence; numerical experiments},
language = {eng},
month = {7},
number = {6},
pages = {1141-1161},
publisher = {EDP Sciences},
title = {A linear scheme to approximate nonlinear cross-diffusion systems*},
url = {http://eudml.org/doc/276354},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Murakawa, Hideki
TI - A linear scheme to approximate nonlinear cross-diffusion systems*
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/7//
PB - EDP Sciences
VL - 45
IS - 6
SP - 1141
EP - 1161
AB - 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.
LA - eng
KW - Cross-diffusion systems; nonlinear diffusion; discrete-time schemes; numerical schemes; Reaction-diffusion system approximations; cross-diffusion systems; reaction-diffusion system; stability; convergence; numerical experiments
UR - http://eudml.org/doc/276354
ER -

References

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