The asymptotic expansion and numerical verification method for linear and nonlinear initial value problem

被引：3

作者：

Hassan, I. H. Abdel-Halim ^{[1
]}

机构：

[1] Zagazig Univ, Fac Sci, Dept Math, Zagazig, Egypt

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 180卷 / 01期

关键词：

asymptotic expansion; linear and nonlinear initial value problems; regular perturbation method; Duffing's equation; Runge-Kutta method;

D O I：

10.1016/j.amc.2005.11.146

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the asymptotic expansion technique is applied to verify the order of accuracy of asymptotic expansion of linear and nonlinear initial value problems. Numerical solutions are obtained to illustrate the preciseness and effectiveness of verifying the validity of asymptotic expansions. (c) 2006 Published by Elsevier Inc.

引用

页码：29 / 37

页数：9

共 7 条

[1] [Anonymous], 1998, Elementary Applied Partial Differential Equations: With Fourier Series and Boundary Value Problems
[2] Bender C.M., 1978, Advanced mathematical methods for scientists and engineers
[3] A technique for the numerical verification of asymptotic expansions
Bosley, DL
[J]. SIAM REVIEW, 1996, 38 (01) : 128 - 135
[4] The asymptotic expansion and numerical verification of Van der Pol's equation
Deeba, E
Xie, SS
[J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2001, 3 (02) : 165 - 171
[5] Kevorkian J., 1981, APPL MATH SCI, V34
[6] Nayfeh AH, 1993, PROBLEMS PERTURBATIO, V2nd
[7] Zwillinger D., 1992, HDB DIFFERENTIAL EQU

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