A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition

IF 0.5 4区数学 Q3 MATHEMATICS

Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI:10.1007/s11253-024-02312-z

Baransel Gunes, Musa Cakir

引用次数: 0

Abstract

We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra-Fredholm integrodifferential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain an approximate solution of the presented problem. It is proved that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method.

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求解带积分边界条件的奇异扰动 Volterra-Fredholm 积分微分方程的拟合近似法

我们考虑了一种新的数值方法，用于求解具有层行为和积分边界条件的二阶 Volterra-Fredholm 微分方程的边界值问题。在合适的 Shishkin 型网格上提出了一种有限差分方案，以获得所提问题的近似解。研究证明，该方法在离散最大规范下具有一阶收敛性。两个数值示例展示了该方法的效率。

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

Ukrainian Mathematical Journal MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

107

审稿时长

4-8 weeks

期刊介绍： Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries. Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.