A numerical approach for solving nonlinear Fredholm integro-differential equation with boundary layer

被引：6
|
作者：
Cakir, Musa [1 ]
Ekinci, Yilmaz [2 ]
Cimen, Erkan [3 ]
机构：
[1] Van Yuzuncu Yil Univ, Fac Sci, Dept Math, TR-65080 Van, Turkey
[2] Van Yuzuncu Yil Univ, Inst Nat & Appl Sci, Dept Math, TR-65080 Van, Turkey
[3] Van Yuzuncu Yil Univ, Fac Educ, Dept Math, TR-65080 Van, Turkey
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2022年 / 41卷 / 06期
关键词：
Singular perturbation; Initial-value problem; Fredholm integro-differential equation; Uniform convergence; Shishkin mesh; COLLOCATION METHOD;
D O I：
10.1007/s40314-022-01933-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The study deals with an initial-value problem for a singularly perturbed nonlinear Fredholm integro-differential equation. Parameter explicit theoretical bounds on the continuous solution and its derivative are derived. To solve the approximate solution to this problem, a new difference scheme is constructed with the finite difference method by using the interpolated quadrature rules with the remaining terms in integral form. Parameter uniform error estimates for the approximate solution are established. It is proved that the method converges in the discrete maximum norm, uniformly with respect to the perturbation parameter. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.
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页数：14
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