A spline method for second-order singularly perturbed boundary-value problems

被引：71

作者：

Aziz, T ^{[1
]}

Khan, A ^{[1
]}

机构：

[1] Aligarh Muslim Univ, Fac Engn & Technol, Dept Appl Math, Aligarh 202002, Uttar Pradesh, India

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2002年 / 147卷 / 02期

关键词：

cubic spline in compression; boundary-layers; monotone matrix; irreducible matrix;

D O I：

10.1016/S0377-0427(02)00479-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a difference scheme based on cubic spline in compression for second-order singularly perturbed boundary value problem of the form ey" = p(x)y' + q(x)y + r(x), y(a) = alpha(0), y(b) = alpha(1). The method is shown to have second- and fourth-order convergence depending on the choice of parameters lambda(1) and lambda(2) involved in the method. The method is tested on an example and the results found to be in agreement with the theory. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：445 / 452

页数：8

共 16 条

[1]

Al-Said E.A., 1998, KOREAN J COMPUT APPL, V5, P759

[2]

Ascher U.M., 1988, NUMERICAL SOLUTION B

[3]

AZIZ AK, 1975, NUMERICAL SOLUTION 2

[4] PIECEWISE CUBIC INTERPOLATION AND 2-POINT BOUNDARY PROBLEMS [J].

BICKLEY, WG .

COMPUTER JOURNAL, 1968, 11 (02) :206-&

[5]

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

[6]

FLAHERTY JE, 1977, MATH COMPUT, V31, P66, DOI 10.1090/S0025-5718-1977-0657396-0

[7] USE OF CUBIC SPLINES IN SOLUTION OF 2-POINT BOUNDARY VALUE PROBLEMS [J].

FYFE, DJ .

COMPUTER JOURNAL, 1969, 12 (02) :188-&

[8]

Henrici P., 1962, Discrete variable methods in ordinary differential equations

[9] Variable-mesh difference scheme for singularly-perturbed boundary-value problems using splines [J].

Kadalbajoo, MK ;

Bawa, RK .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1996, 90 (02) :405-416

[10] ASYMPTOTIC AND NUMERICAL-ANALYSIS OF SINGULAR PERTURBATION PROBLEMS - A SURVEY [J].

KADALBAJOO, MK ;

REDDY, YN .

APPLIED MATHEMATICS AND COMPUTATION, 1989, 30 (03) :223-259

← 1 2 →