Adaptation of homotopy analysis method for the numeric-analytic solution of Chen system

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42 Citations (Scopus)

Abstract

In this paper, a new reliable algorithm based on an adaptation of the standard homotopy analysis method (HAM) is presented, which is the multistage homotopy analysis method (MSHAM). The freedom of choosing the auxiliary linear operator and the auxiliary parameter are still present in the MSHAM. The solutions of the non-chaotic and the chaotic Chen system which is a three-dimensional system of ordinary differential equations with quadratic nonlinearities were obtained by MSHAM. Numerical comparisons between the MSHAM and the classical fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for solving the non-linear chaotic and non-chaotic Chen system.

Original languageEnglish
Pages (from-to)2336-2346
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume14
Issue number5
DOIs
Publication statusPublished - May 2009

Fingerprint

Chen System
Homotopy Analysis Method
Chaotic systems
Numerics
Analytic Solution
Ordinary differential equations
Numerical Comparisons
Runge-Kutta
System of Ordinary Differential Equations
Chaotic System
Linear Operator
Fourth Order
Numerical Solution
Nonlinearity
Three-dimensional

Keywords

  • Chen system
  • Fourth-order Runge-Kutta method
  • Homotopy analysis method
  • Multistage homotopy analysis method

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

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title = "Adaptation of homotopy analysis method for the numeric-analytic solution of Chen system",
abstract = "In this paper, a new reliable algorithm based on an adaptation of the standard homotopy analysis method (HAM) is presented, which is the multistage homotopy analysis method (MSHAM). The freedom of choosing the auxiliary linear operator and the auxiliary parameter are still present in the MSHAM. The solutions of the non-chaotic and the chaotic Chen system which is a three-dimensional system of ordinary differential equations with quadratic nonlinearities were obtained by MSHAM. Numerical comparisons between the MSHAM and the classical fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for solving the non-linear chaotic and non-chaotic Chen system.",
keywords = "Chen system, Fourth-order Runge-Kutta method, Homotopy analysis method, Multistage homotopy analysis method",
author = "Alomari, {A. K.} and {Md. Noorani}, {Mohd. Salmi} and {Mohd. Nazar}, Roslinda",
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AU - Alomari, A. K.

AU - Md. Noorani, Mohd. Salmi

AU - Mohd. Nazar, Roslinda

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N2 - In this paper, a new reliable algorithm based on an adaptation of the standard homotopy analysis method (HAM) is presented, which is the multistage homotopy analysis method (MSHAM). The freedom of choosing the auxiliary linear operator and the auxiliary parameter are still present in the MSHAM. The solutions of the non-chaotic and the chaotic Chen system which is a three-dimensional system of ordinary differential equations with quadratic nonlinearities were obtained by MSHAM. Numerical comparisons between the MSHAM and the classical fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for solving the non-linear chaotic and non-chaotic Chen system.

AB - In this paper, a new reliable algorithm based on an adaptation of the standard homotopy analysis method (HAM) is presented, which is the multistage homotopy analysis method (MSHAM). The freedom of choosing the auxiliary linear operator and the auxiliary parameter are still present in the MSHAM. The solutions of the non-chaotic and the chaotic Chen system which is a three-dimensional system of ordinary differential equations with quadratic nonlinearities were obtained by MSHAM. Numerical comparisons between the MSHAM and the classical fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for solving the non-linear chaotic and non-chaotic Chen system.

KW - Chen system

KW - Fourth-order Runge-Kutta method

KW - Homotopy analysis method

KW - Multistage homotopy analysis method

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