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Additive schemes based domain decomposition algorithm for solving singularly perturbed parabolic reaction-diffusion systems
Computational and Applied Mathematics ( IF 2.998 ) Pub Date : 2021-03-12 , DOI: 10.1007/s40314-021-01457-y
Aakansha , Joginder Singh , Sunil Kumar

In this paper, we examine a 1D parabolic coupled system of singularly perturbed reaction-diffusion problems in which perturbation parameters can be of distinct magnitude. To solve this system numerically we develop additive (or splitting) schemes based domain decomposition algorithm of Schwarz waveform relaxation type. On each subdomain we consider two additive schemes on a uniform mesh in time and the standard central difference scheme on a uniform mesh in space. We provide convergence analysis of the algorithm using some auxiliary problems and the algorithm is shown to be uniformly convergent. The additive schemes make the computation more efficient as they decouple the components of the approximate solution at each time level. Numerical results for two test problems are given in support of the theoretical convergence result and as well as to illustrate the efficiency of the additive schemes.



中文翻译:

基于加性方案的域分解算法求解奇摄动抛物线反应扩散系统

在本文中,我们研究了一维抛物线耦合系统,该系统具有奇异摄动反应扩散问题,其中摄动参数的大小可能不同。为了从数值上解决该系统,我们开发了基于加法(或分裂)方案的Schwarz波形弛豫类型的域分解算法。在每个子域上,我们考虑时间上均匀网格上的两个加法方案和空间上均匀网格上的标准中心差方案。我们使用一些辅助问题提供了算法的收敛性分析,并且证明该算法是一致收敛的。加性方案在每个时间级别解耦近似解决方案的组成部分时,使计算效率更高。

更新日期:2021-03-12
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