An adaptive splitting approach for the quenching solution of reaction-diffusion equations over nonuniform grids

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:241

Article

Beauregard, Matthew A.¹ 

[1] Baylor Univ, Dept Math, Waco, TX 76798 USA

关键词: Reaction-diffusion equations;    Quenching singularity;    Degeneracy;    Splitting method;    Adaptation;    Nonuniform grids;   

DOI  :  10.1016/j.cam.2012.10.005

来源: Elsevier

【 摘 要 】

The numerical solution of a nonlinear degenerate reaction-diffusion equation of the quenching type is investigated. While spatial derivatives are discretized over symmetric nonuniform meshes, a Peaceman-Rachford splitting method is employed to advance solutions of the semidiscretized system. The temporal step is determined adaptively through a suitable arc-length monitor function. A criterion is derived to ensure that the numerical solution acquired preserves correctly the positivity and monotonicity of the analytical solution. Weak stability is proven in a von Neumann sense via the infinity-norm. Computational examples are presented to illustrate our results. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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