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

被引：14
|
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.
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页码：505 / 528
页数：24
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