用拟合算子格式数值处理抛物型奇摄动微分差分方程

Q3 Mathematics
D. Tefera, A. Tiruneh, G. A. Derese
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引用次数: 3

摘要

本文提出了求解空间变量上有时滞的奇异摄动抛物型偏微分方程的一种新的拟合算子策略。我们把这个问题分解成三个分段方程。方程中的延迟项采用泰勒级数展开,时间变量采用隐式欧拉法离散,空间变量采用中心差分法离散。在发展了拟合算子方法后,采用Richardson外推格式加快了时间方向的收敛阶数,得到了一致的收敛阶数。最后,通过三个算例说明了该方法的有效性。结果表明,本文提出的方法比现有的一些方法精度更高。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme
This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. We decomposed the problem into three piecewise equations. The delay term in the equation is expanded by Taylor series, the time variable is discretized by implicit Euler method, and the space variable is discretized by central difference methods. After developing the fitting operator method, we accelerate the order of convergence of the time direction using Richardson extrapolation scheme and obtained uniform order of convergence. Finally, three examples are given to illustrate the effectiveness of the method. The result shows the proposed method is more accurate than some of the methods that exist in the literature.
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
36
审稿时长
3.5 months
期刊介绍: Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.
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