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

被引：23
作者：
Beauregard, Matthew A. [1 ]
Sheng, Qin
机构：
[1] Baylor Univ, Dept Math, Waco, TX 76798 USA
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2013年 / 241卷
关键词：
Reaction-diffusion equations; Quenching singularity; Degeneracy; Splitting method; Adaptation; Nonuniform grids; BLOW-UP; THEOREM;
D O I：
10.1016/j.cam.2012.10.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
引用
收藏
页码：30 / 44
页数：15
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