Application of multistage homotopy-perturbation method for the solutions of the Chen system

M. S H Chowdhury, Ishak Hashim

Research output: Contribution to journalArticle

56 Citations (Scopus)

Abstract

In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chen system. We shall call this technique as the multistage HPM (for short MHPM). In particular we look at the accuracy of the HPM as the Chen system changes from a nonchaotic system to a chaotic one. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear chaotic and nonchaotic systems of ODEs.

Original languageEnglish
Pages (from-to)381-391
Number of pages11
JournalNonlinear Analysis: Real World Applications
Volume10
Issue number1
DOIs
Publication statusPublished - Feb 2009

Fingerprint

Chen System
Homotopy Perturbation Method
Numerical Comparisons
Runge-Kutta
Fourth Order
Approximate Solution
Numerical Solution
Nonlinearity
Three-dimensional
Interval
Homotopy perturbation method

Keywords

  • Chaos, Homotopy-perturbation method
  • Chen system
  • Fourth-order Runge-Kutta method

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Mathematics(all)
  • Modelling and Simulation
  • Engineering (miscellaneous)

Cite this

Application of multistage homotopy-perturbation method for the solutions of the Chen system. / Chowdhury, M. S H; Hashim, Ishak.

In: Nonlinear Analysis: Real World Applications, Vol. 10, No. 1, 02.2009, p. 381-391.

Research output: Contribution to journalArticle

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