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

被引：19

作者：

Durmaz, Muhammet Enes ^{[1
]}

Amirali, Ilhame ^{[2
]}

Amiraliyev, Gabil M. ^{[3
]}

机构：

[1] Kirklareli Univ, Dept Informat Technol, TR-39100 Kirklareli, Turkey

[2] Duzce Univ, Fac Arts & Sci, Dept Math, TR-81620 Duzce, Turkey

[3] Erzincan Binali Yildirim Univ, Fac Arts & Sci, Dept Math, TR-24100 Erzincan, Turkey

来源：

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2023年 / 69卷 / 01期

关键词：

Finite difference scheme; Fredholm integro-differential equation; Integral boundary condition; Shishkin mesh; Singular perturbation; Uniform convergence; DIFFERENCE METHOD;

D O I：

10.1007/s12190-022-01757-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：505 / 528

页数：24

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