Variational iteration method as a reliable treatment for the hyperchaotic rössler system

S. M. Goh, Mohd. Salmi Md. Noorani, Ishak Hashim, M. Mossa Al-Sawalha

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

This paper concerns the implementation of variational iteration method (VIM) in solving the hyperchaotic Rössler analytically. It is a four dimensional system of ODEs with quadratic nonlinearities. The computation was made using a newly found version called the multistage VIM (MVIM) which offers some slight modification to the traditional VIM. Numerical comparisons are made between MVIM and the classical fourth-order Runge-Kutta (RK4) with results displaying extremely good performance by MVIM, yielding great accuracy and efficiency. It is also evident that MVIM surpasses (in terms of accuracy) its two counterparts, the Adomian decomposition method (ADM) and Differential transformation method (DTM).

Original languageEnglish
Pages (from-to)363-371
Number of pages9
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
Volume10
Issue number3
Publication statusPublished - 2009

Fingerprint

Hyperchaotic System
Variational Iteration Method
iteration
Decomposition
Differential Transformation Method
Adomian Decomposition Method
Numerical Comparisons
Runge-Kutta
nonlinearity
Fourth Order
decomposition
Nonlinearity

Keywords

  • Hyperchaotic
  • Rössler system
  • Runge-kutta method
  • Variational iteration method

ASJC Scopus subject areas

  • Modelling and Simulation
  • Physics and Astronomy(all)
  • Applied Mathematics
  • Computational Mechanics
  • Mechanics of Materials
  • Statistical and Nonlinear Physics
  • Engineering (miscellaneous)

Cite this

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AB - This paper concerns the implementation of variational iteration method (VIM) in solving the hyperchaotic Rössler analytically. It is a four dimensional system of ODEs with quadratic nonlinearities. The computation was made using a newly found version called the multistage VIM (MVIM) which offers some slight modification to the traditional VIM. Numerical comparisons are made between MVIM and the classical fourth-order Runge-Kutta (RK4) with results displaying extremely good performance by MVIM, yielding great accuracy and efficiency. It is also evident that MVIM surpasses (in terms of accuracy) its two counterparts, the Adomian decomposition method (ADM) and Differential transformation method (DTM).

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