Numerical methods for nonlinear fourth-order boundary value problems with applications

Mohamed Ali Hajji, Kamel Al-Khaled

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we present efficient numerical algorithms for the approximate solution of nonlinear fourth-order boundary value problems. The first algorithm deals with the sinc-Galerkin method (SGM). The sinc basis functions prove to handle well singularities in the problem. The resulting SGM discrete system is carefully developed. The second method, the Adomian decomposition method (ADM), gives the solution in the form of a series solution. A modified form of the ADM based on the use of the Laplace transform is also presented. We refer to this method as the Laplace Adomian decomposition technique (LADT). The proposed LADT can make the Adomian series solution convergent in the Laplace domain, when the ADM series solution diverges in the space domain. A number of examples are considered to investigate the reliability and efficiency of each method. Numerical results show that the sinc-Galerkin method is more reliable and more accurate.

Original languageEnglish
Pages (from-to)83-104
Number of pages22
JournalInternational Journal of Computer Mathematics
Volume85
Issue number1
DOIs
Publication statusPublished - Jan 2008

Fingerprint

Sinc Method
Fourth-order Boundary Value Problem
Adomian Decomposition Method
Series Solution
Nonlinear Boundary Value Problems
Laplace
Galerkin Method
Adomian Decomposition
Boundary value problems
Numerical methods
Decomposition Techniques
Numerical Methods
Decomposition
Galerkin methods
Sinc Function
Diverge
Discrete Systems
Numerical Algorithms
Laplace transform
Basis Functions

Keywords

  • Adomian's decomposition method
  • Approximate solutions
  • Fourth order BVPs
  • Laplace transform
  • Sinc-Galerkin

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Numerical methods for nonlinear fourth-order boundary value problems with applications. / Hajji, Mohamed Ali; Al-Khaled, Kamel.

In: International Journal of Computer Mathematics, Vol. 85, No. 1, 01.2008, p. 83-104.

Research output: Contribution to journalArticle

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