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Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

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  • Daniel Olvera
  • Alex Elías-Zúñiga

Abstract

We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM) that is based on the homotopy perturbation method (HPM) and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM). At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge‐Kutta method via the amplitude‐time response curves.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:486509
    DOI: 10.1155/2014/486509
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    References listed on IDEAS

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    1. Abdon Atangana & Necdet Bildik & S. C. Oukouomi Noutchie, 2014. "New Iteration Methods for Time-Fractional Modified Nonlinear Kawahara Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, January.
    2. 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, Hindawi, vol. 2012, pages 1-10, May.
    3. Abdon Atangana & Necdet Bildik & S. C. Oukouomi Noutchie, 2014. "New Iteration Methods for Time‐Fractional Modified Nonlinear Kawahara Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. 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).
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    Cited by:

    1. D. Olvera & A. Elías-Zúñiga & L. N. López de Lacalle & C. A. Rodríguez, 2015. "Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

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