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Zbl 1246.65241
Chowdhury, M.S.H.; Hashim, I.; Momani, S.; Rahman, M.M.
Application of multistage homotopy perturbation method to the chaotic Genesio system. (English)
[J] Abstr. Appl. Anal. 2012, Article ID 974293, 10 p. (2012). ISSN 1085-3375; ISSN 1687-0409/e

Summary: Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM) is applied to the chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM). The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4) solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.

MSC 2000:: *65P20 Numerical chaos
37D45 Strange attractors, chaotic dynamics
37N35 Dynamical systems in control

Keywords: chaotic system; homotopy-perturbation method; algorithm; numerical comparisons; Runge-Kutta

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Zentralblatt MATH Berlin [Germany]