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Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System

Author

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  • M. S. H. Chowdhury
  • I. Hashim
  • S. Momani
  • M. M. Rahman

Abstract

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.

Suggested Citation

  • M. S. H. Chowdhury & I. Hashim & S. Momani & M. M. Rahman, 2012. "Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:974293
    DOI: 10.1155/2012/974293
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    References listed on IDEAS

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    1. Hashim, I. & Chowdhury, M.S.H. & Mawa, S., 2008. "On multistage homotopy-perturbation method applied to nonlinear biochemical reaction model," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 823-827.
    2. Chowdhury, M.S.H. & Hashim, I. & Momani, S., 2009. "The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1929-1937.
    3. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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    4. Daniel Olvera & Alex Elías-Zúñiga, 2014. "Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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