A uniform numerical method for dealing with a singularly perturbed delay initial value problem

被引：43

作者：

Amiraliyeva, I. G. ^{[1
]}

Erdogan, F. ^{[2
]}

Amiraliyev, G. M. ^{[1
]}

机构：

[1] Sinop Univ, Fac Sci, Dept Math, TR-57000 Sinop, Turkey

[2] Yuzuncu Yil Univ, Fac Art & Sci, Dept Math, TR-65080 Van, Turkey

来源：

APPLIED MATHEMATICS LETTERS | 2010年 / 23卷 / 10期

关键词：

Delay differential equation; Singular perturbation; Exponentially fitted difference scheme; Uniformly convergent; Error estimates; BOUNDARY-VALUE-PROBLEMS; DIFFERENCE; EQUATIONS;

D O I：

10.1016/j.aml.2010.06.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work deals with a singularly perturbed initial value problem fora quasi-linear second-order delay differential equation. An exponentially fitted difference scheme is constructed, in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm. Numerical results are also presented. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1221 / 1225

页数：5

共 17 条

[1] A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations [J].

Amiraliyev, Gabil M. ;

Erdogan, Fevzi .

NUMERICAL ALGORITHMS, 2009, 52 (04) :663-675

[2] A uniformly convergent finite difference method for a singularly perturbed initial value problem [J].

Amiraliyev, GM ;

Duru, H .

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 1999, 20 (04) :379-387

[3]

Amiraliyev GM., 1995, Turkish J. Math, V19, P207

[4]

[Anonymous], 2003, Numerical Methods for Delay Differential Equations

[5]

Bellman R.E., 1963, Differential-Difference Equations, V6

[6] BIFURCATION GAP IN A HYBRID OPTICALLY BISTABLE SYSTEM [J].

DERSTINE, MW ;

GIBBS, HM ;

HOPF, FA ;

KAPLAN, DL .

PHYSICAL REVIEW A, 1982, 26 (06) :3720-3722

[7]

Driver RD, 1977, APPLMATH SCI

[8]

Farrell P., 2000, Robust Computational Techniques for Boundary Layers

[9] A numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations [J].

Kadalbajoo, Mohan K. ;

Sharma, Kapil K. .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 197 (02) :692-707

[10] SINGULAR PERTURBATION ANALYSIS OF BOUNDARY-VALUE-PROBLEMS FOR DIFFERENTIAL-DIFFERENCE EQUATIONS .6. SMALL SHIFTS WITH RAPID OSCILLATIONS [J].

LANGE, CG ;

MIURA, RM .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1994, 54 (01) :273-283

← 1 2 →