Fitted Operator Average Finite Difference Method for Singularly Perturbed Delay Parabolic Reaction Diffusion Problems with Non-Local Boundary Conditions

IF 0.7 Q2 MATHEMATICS
Wakjira Tolassa Gobena, G. Duressa
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引用次数: 5

Abstract

This paper deals with numerical solution of singularly perturbed delay parabolic reaction diffusion problem having large delay on the spatial variable with non-local boundary condition. The solution of the problem exhibits parabolic boundary layer on both sides of the spatial domain and interior layer is also created. Introducing a fitting parameter into asymptotic solution and applying average finite difference approximation, a fitted operator finite difference method is developed for solving the problem under consideration. To treat the non-local boundary condition, Simpson's rule is applied. The stability and $\varepsilon$ uniform convergence analysis has been carried out. To validate the applicability of the scheme, numerical examples are presented and solved for different values of the perturbation parameter $\varepsilon$ and mesh sizes. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and shown to be second order Uniformly convergent in both direction, and it also improves the results of the methods existing in the literature.
非局部边界条件下奇摄动时滞抛物型反应扩散问题的拟合算子平均有限差分法
研究了具有非局部边界条件的空间变量上具有大时滞的奇摄动时滞抛物型反应扩散问题的数值解。该问题的解在空间域两侧有抛物线边界层,并建立了内层。在渐近解中引入拟合参数,应用平均有限差分逼近,提出了一种拟合算子有限差分法。采用辛普森规则处理非局部边界条件。并对其稳定性和一致收敛性进行了分析。为了验证该格式的适用性,给出了数值算例,并对不同的扰动参数$\varepsilon$和网格尺寸进行了求解。数值结果以最大绝对误差和收敛速度的形式列示,结果表明,本文方法在两个方向上都是二阶均匀收敛的,并且改进了文献中已有方法的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.50
自引率
0.00%
发文量
11
期刊介绍: To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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