# A linear scheme to approximate nonlinear cross-diffusion systems*

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

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

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topMurakawa, 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 -

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