On a fourth-order finite-difference method for singularly perturbed boundary value problems

被引：7

作者：

Herceg, Dragoslav ^{[1
]}

Herceg, Djordje ^{[1
]}

机构：

[1] Univ Novi Sad, Fac Sci, Dept Math & Informat, Novi Sad 21000, Serbia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 203卷 / 02期

关键词：

finite differences; boundary value problem; nonequidistant mesh; singular perturbation;

D O I：

10.1016/j.amc.2008.05.103

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a fourth-order finite-difference method for singularly perturbed one-dimensional reaction-diffusion problem. The problem is discretized using a Bakhvalov-type mesh. We give a uniform convergence with respect to the perturbation parameter. Numerical examples are presented which demonstrate computationally the fourth order of the method. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：828 / 837

页数：10

共 21 条

[1]

[Anonymous], ZB RAD PRIR MAT FA M

[2]

BAKHVALOV NS, 1969, USSR COMP MATH MATH+, V9, P841

[3]

BOGLAEV IP, 1981, ZH VYCH MAT MAT FIZ, V21, P887

[4] 4TH-ORDER FINITE-DIFFERENCE METHODS FOR 2-POINT BOUNDARY-VALUE-PROBLEMS [J].

BOGUCZ, EA ;

WALKER, JDA .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1984, 4 (01) :69-82

[5]

BOHL E, 1981, FINITE MODELLE GEWOH

[6] High order methods for elliptic and time dependent reaction-diffusion singularly perturbed problems [J].

Clavero, C ;

Gracia, JL .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 168 (02) :1109-1127

[7] UNIFORM-CONVERGENCE OF ARBITRARY ORDER ON NONUNIFORM MESHES FOR A SINGULARLY PERTURBED BOUNDARY-VALUE PROBLEM [J].

CLAVERO, C ;

LISBONA, F ;

MILLER, JJH .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1995, 59 (02) :155-171

[8]

DEUFLHARD P, 1982, 163 U HEID I ANG INF

[9]

DIECKHOFF HJ, 1975, 7520 TU MUNCH I MATH

[10]

Doolan E.P., 1980, Uniform Numerical Methods for Problems with Initial and Boundary Layers

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