Comparing numerical methods for the solutions of the Chen system

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39 Citations (Scopus)

Abstract

In this paper, the Adomian decomposition method (ADM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta (RK4) numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given.

Original languageEnglish
Pages (from-to)1296-1304
Number of pages9
JournalChaos, Solitons and Fractals
Volume32
Issue number4
DOIs
Publication statusPublished - May 2007

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Chen System
Adomian Decomposition Method
Numerical Methods
decomposition
Lorenz System
Infinite series
Runge-Kutta
Power series
Lyapunov Exponent
Fourth Order
Analytical Solution
power series
Numerical Solution
Nonlinearity
Decompose
Three-dimensional
nonlinearity
exponents
Term

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics

Cite this

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title = "Comparing numerical methods for the solutions of the Chen system",
abstract = "In this paper, the Adomian decomposition method (ADM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta (RK4) numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given.",
author = "{Md. Noorani}, {Mohd. Salmi} and Ishak Hashim and Ahmad, {Rokiah @ Rozita} and {Abu Bakar}, Sakhinah and Ismail, {Eddie Shahril} and Zakaria, {A. M.}",
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T1 - Comparing numerical methods for the solutions of the Chen system

AU - Md. Noorani, Mohd. Salmi

AU - Hashim, Ishak

AU - Ahmad, Rokiah @ Rozita

AU - Abu Bakar, Sakhinah

AU - Ismail, Eddie Shahril

AU - Zakaria, A. M.

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AB - In this paper, the Adomian decomposition method (ADM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta (RK4) numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given.

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