A fully adaptive approximation for quenching‐type reaction‐diffusion equations over circular domains
A fully adaptive approximation for quenching‐type reaction‐diffusion equations over circular domains
复制标题
圆域猝灭型反应扩散方程的完全自适应近似
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Q. Sheng
中科院分区：
文献类型：
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作者：
M. Beauregard;Q. Sheng
本文研究了一种完全自适应有限差分方法，用于求解圆形域上的猝灭型非线性反应扩散方程。尽管在原点和径向对称性上施加了辅助条件，但自适应是分别通过基于弧长的空间和时间监控函数来完成的。在适当的网格约束下，证明了数值解的单调性和正性，并保证了冯诺依曼意义上的数值稳定性。获得临界淬火半径的理论界限，然后通过计算进行细化。提供计算示例来说明所开发的新自适应计算程序的有效性和合理性。 © 2013 Wiley periodicals, Inc. 数值方法偏微分方程 30: 472–489, 2014
This article studies a fully adaptive finite difference method for solving quenching‐type nonlinear reaction‐diffusion equations over circular domains. Although an auxiliary condition at the origin and radial symmetry are imposed, adaptations are accomplished via arc‐length‐based monitoring functions in space and time, respectively. The monotonicity and positivity of the numerical solution are proved following a suitable grid constraint, and the numerical stability is ensured in the von Neumann sense. Theoretical bounds of the critical quenching radius are obtained and then refined through the computation. Computational examples are provided to illustrate the effectiveness and plausibility of the new adaptive computational procedure developed. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 472–489, 2014