A Parameter-Uniform First Order Convergent Numerical Method for a Semi-linear System of Singularly Perturbed Second Order Delay Differential Equations

被引：0

作者：

Manikandan, Mariappan ^{[1
]}

Miller, John J. H. ^{[2
]}

Sigamani, Valarmathi ^{[1
]}

机构：

[1] Bishop Heber Coll, Dept Math, Tiruchirappalli, Tamil Nadu, India

[2] Trinity Coll Dublin, Dublin, Ireland

来源：

DIFFERENTIAL EQUATIONS AND NUMERICAL ANALYSIS | 2016年 / 172卷

关键词：

Singular perturbation problems; Boundary and interior layers; Semilinear delay-differential equations; Finite difference scheme; Shishkin mesh; Parameter-uniform convergence;

D O I：

10.1007/978-81-322-3598-9_9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a boundary value problem for a semi-linear system of two singularly perturbed second order delay differential equations is considered on the interval (0, 2). The components of the solution of this system exhibit boundary layers at x = 0 and x = 2 and interior layers at x = 1. A numerical method composed of a classical finite difference operator applied on a piecewise uniform Shishkin mesh is suggested to solve the problem. The method is proved to be first order convergent in the maximum norm uniformly in the perturbation parameters. Numerical computation is described, which supports the theoretical results.

引用

页码：151 / 165

页数：15

共 50 条

[1] A Parameter-Uniform First Order Convergent Numerical Method for a System of Singularly Perturbed Second Order Delay Differential Equations
Mariappan, Manikandan
Miller, John J. H.
Sigamani, Valarmathi
[J]. BOUNDARY AND INTERIOR LAYERS, COMPUTATIONAL AND ASYMPTOTIC METHODS - BAIL 2014, 2015, 108 : 183 - 195
[2] A uniformly almost second order convergent numerical method for singularly perturbed delay differential equations
Erdogan, Fevzi
Cen, Zhongdi
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 333 : 382 - 394
[3] Second order parameter-uniform numerical method for a partially singularly perturbed linear system of reaction-diffusion type
Paramasivam, Mathiyazhagan
Miller, John J. H.
Valarmathi, Sigamani
[J]. MATHEMATICAL COMMUNICATIONS, 2013, 18 (01) : 271 - 295
[4] SECOND ORDER PARAMETER-UNIFORM CONVERGENCE FOR A FINITE DIFFERENCE METHOD FOR A SINGULARLY PERTURBED LINEAR PARABOLIC SYSTEM
Franklin, V.
Paramasivam, M.
Miller, J. J. H.
Valarmathi, S.
[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2013, 10 (01) : 178 - 202
[5] First Order Parameter Uniform Numerical Method for a System of Two Singularly Perturbed Delay Differential Equations with Robin Initial Conditions
Praveena, R.
Paramasivam, M. Joseph
[J]. JOURNAL OF ALGEBRAIC STATISTICS, 2022, 13 (02) : 1063 - 1071
[6] High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay
Kumar, Sunil
Kumar, Mukesh
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2014, 68 (10) : 1355 - 1367
[7] Second order parameter-uniform convergence for a finite difference method for a partially singularly perturbed linear parabolic system
Franklin, Victor
Miller, John J. H.
Valarmathi, Sigamani
[J]. MATHEMATICAL COMMUNICATIONS, 2014, 19 (03) : 469 - 495
[8] Second-order uniformly convergent numerical method for singularly perturbed delay parabolic partial differential equations
Das, Abhishek
Natesan, Srinivasan
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (03) : 490 - 510
[9] Second order parameter-uniform convergence for a finite direrence method for a singularly perturbed linear reaction-diffusion system
Mathiyazhagan, Paramasivam
Sigamani, Valarmathi
Miller, John J. H.
[J]. MATHEMATICAL COMMUNICATIONS, 2010, 15 (02) : 587 - 612
[10] Parameter-Uniform Convergent Numerical Approach for Time-Fractional Singularly Perturbed Partial Differential Equations With Large Time Delay
Kumie, Habtamu Getachew
Tiruneh, Awoke Andargie
Derese, Getachew Adamu
[J]. COMPUTATIONAL AND MATHEMATICAL METHODS, 2024, 2024

← 1 2 3 4 5 →