A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems

被引：48

作者：

Geng, Fazhan ^{[1
]}

机构：

[1] Changshu Inst Technol, Dept Math, Changshu 215500, Jiangsu, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 213卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Nonlinear; Fourth-order boundary value problem; New reproducing kernel Hilbert space method; EQUATION;

D O I：

10.1016/j.amc.2009.02.053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems. It is a relatively new analytical technique. The solution obtained by using the method takes the form of a convergent series with easily computable components. This paper will present a numerical comparison between our method and other methods for solving an open fourth-order boundary value problem presented by Scott and Watts. The method is also applied to a nonlinear fourth-order boundary value problem. The numerical results demonstrate that the new method is quite accurate and efficient for fourth-order boundary value problems. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：163 / 169

页数：7

共 20 条

[11] Solving a nonlinear system of second order boundary value problems [J].

Geng, Fazhan ;

Cui, Minggen .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (02) :1167-1181

[12]

GENG FZ, 2008, J KOREAN MATH SOC, V45

[13] The exact solution for solving a class nonlinear operator equations in the reproducing kernel space [J].

Li, CL ;

Cui, MG .

APPLIED MATHEMATICS AND COMPUTATION, 2003, 143 (2-3) :393-399

[14] Iterative solutions for a beam equation with nonlinear boundary conditions of third order [J].

Ma, TF ;

da Silva, J .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 159 (01) :11-18

[15] Homotopy perturbation method for solving fourth-order boundary value problems [J].

Mohyud-Din, Syed Tauseef ;

Noor, Muhammad Aslam .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2007, 2007

[16]

Momani S. M, 1991, THESIS WALSE U UK

[17] Numerical comparison of methods for solving a special fourth-order boundary value problem [J].

Momani, Shaher ;

Noor, Muhammad Aslam .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 191 (01) :218-224

[18] Variational iteration technique for solving higher order boundary value problems [J].

Noor, Muhammad Aslam ;

Mohyud-Din, Syed Tauseef .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 189 (02) :1929-1942

[19]

SCOTT MR, 1975, SAND750198 SAND LAB

[20] The numerical solution of special fourth-order boundary value problems by the modified decomposition method [J].

Wazwaz, AM .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2002, 79 (03) :345-356

← 1 2 →