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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 974293, 10 pages
Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
1Deptartment of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, 53100 Kuala Lumpur, Malaysia
2School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi Selangor, Malaysia
3Department of Mathematics, The University of Jordan, Amman 11942, Jordan
4Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 Selangor, Malaysia
Received 31 December 2011; Accepted 9 March 2012
Academic Editor: Muhammad Aslam Noor
Copyright © 2012 M. S. H. Chowdhury et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. Genesio and A. Tesi, “Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems,” Automatica, vol. 28, no. 3, pp. 531–548, 1992.
- J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000.
- M. J. Ablowitz, B. M. Herbst, and C. Schober, “Homotopy perturbation method and axisymmetric flow over a stretching sheet,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 4, pp. 399–406, 2006.
- L. Cveticanin, “The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity,” Journal of Sound and Vibration, vol. 285, no. 4-5, pp. 1171–1179, 2005.
- J. H. He, Non-Perturbative Methods for Strongly Nonlinear Problems, Die Deutsche Bibliothek, Berlin, Germany, 2006.
- J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006.
- M. A. Noor and S. T. Mohyud-Din, “An efficient algorithm for solving fifth-order boundary value problems,” Mathematical and Computer Modelling, vol. 45, no. 7-8, pp. 954–964, 2007.
- M. El-Shahed, “Application of He's homotopy perturbation method to Volterra's integro-differential equation,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 6, no. 2, pp. 163–168, 2005.
- J. H. He, “Analytical methods for thermal science-an elementary introduction,” Thermal Science, vol. 15, supplement 1, pp. S1–S3, 2011.
- H. E. Ji-Huan, “A note on the homotopy perturbation method,” Thermal Science, vol. 14, no. 2, pp. 565–568, 2010.
- M. S. H. Chowdhury, I. Hashim, and S. Momani, “The multistage homotopy-perturbation method: a powerful scheme for handling the Lorenz system,” Chaos, Solitons and Fractals, vol. 40, no. 4, pp. 1929–1937, 2009.
- M. S. H. Chowdhury and I. Hashim, “Application of multistage homotopy-perturbation method for the solutions of the Chen system,” Nonlinear Analysis. Real World Applications, vol. 10, no. 1, pp. 381–391, 2009.
- I. Hashim and M. S. H. Chowdhury, “Adaptation of homotopy-perturbation method for numeric-analytic solution of system of ODEs,” Physics Letters A, vol. 372, no. 4, pp. 470–481, 2008.
- I. Hashim, M. S. H. Chowdhury, and S. Mawa, “On multistage homotopy-perturbation method applied to nonlinear biochemical reaction model,” Chaos, Solitons and Fractals, vol. 36, no. 4, pp. 823–827, 2008.