Reliable algorithms for solving integro-differential equations with applications

Ameen Alawneh, Kamel Al-Khaled, Mohammed Al-Towaiq

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This paper suggests four different methods to solve nonlinear integro-differential equations, namely, He's variational iteration method, Adomian decomposition method, He's homotopy perturbation method and differential transform method. To assess the accuracy of each method, a test example with known exact solution is used. The study outlines significant features of these methods as well as sheds some light on advantages of one method over the other. The results show that these methods are very efficient, convenient and can be adapted to fit a larger class of problems. The comparison reveals that, although the numerical results of these methods are similar, He's homotopy perturbation method is the easiest, the most efficient and convenient. Moreover, we applied modified forms of He's variational iteration method and differential transform method to solve a mathematical model, which describes the accumulated effect of toxins on populations living in a closed system.

Original languageEnglish
Pages (from-to)1538-1554
Number of pages17
JournalInternational Journal of Computer Mathematics
Volume87
Issue number7
DOIs
Publication statusPublished - Jun 2010

Fingerprint

Integrodifferential equations
Integro-differential Equation
Mathematical models
Decomposition
Differential Transform Method
Variational Iteration Method
Homotopy Perturbation Method
Nonlinear Integro-differential Equations
Adomian Decomposition Method
Exact Solution
Mathematical Model
Closed
Numerical Results

Keywords

  • Adomian decomposition method
  • Differential transform method
  • Homotopy perturbation method
  • Nonlinear integro-differential equations
  • Population growth
  • Variational iteration method

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

Reliable algorithms for solving integro-differential equations with applications. / Alawneh, Ameen; Al-Khaled, Kamel; Al-Towaiq, Mohammed.

In: International Journal of Computer Mathematics, Vol. 87, No. 7, 06.2010, p. 1538-1554.

Research output: Contribution to journalArticle

Alawneh, Ameen ; Al-Khaled, Kamel ; Al-Towaiq, Mohammed. / Reliable algorithms for solving integro-differential equations with applications. In: International Journal of Computer Mathematics. 2010 ; Vol. 87, No. 7. pp. 1538-1554.
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