一种用于求解具有积分边界条件的奇异摄动Fredholm积分微分方程的高效数值方法。

An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition.

作者信息

Durmaz Muhammet Enes, Amirali Ilhame, Amiraliyev Gabil M

机构信息

Department of Information Technology, Kırklareli University, Kırklareli, 39100 Turkey.

Department of Mathematics, Faculty of Arts and Sciences, Düzce University, Düzce, 81620 Turkey.

出版信息

J Appl Math Comput. 2023;69(1):505-528. doi: 10.1007/s12190-022-01757-4. Epub 2022 Jun 9.

DOI:10.1007/s12190-022-01757-4

PMID:35698573

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9178336/

Abstract

In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in the initial condition. The proposed technique acquires a uniform second-order convergence in respect to perturbation parameter. Further provided the numerical results to support the theoretical estimates.

摘要

本文研究了一个带有积分条件的线性奇异摄动Fredholm积分微分初值问题。在一个Shishkin型网格上，采用拟合有限差分法，在方程的积分部分和初始条件中都使用复合梯形法则。所提出的技术在摄动参数方面具有一致的二阶收敛性。此外还给出了数值结果以支持理论估计。