Reliable algorithms for solving integro-differential equations with applications

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

Research output: Contribution to journalArticle

9 Citations (Scopus)


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
Issue number7
Publication statusPublished - Jun 2010


  • 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

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