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Rational Homotopy Perturbation Method

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  • Héctor Vázquez-Leal

Abstract

The solution methods of nonlinear differential equations are very important because most of the physical phenomena are modelled by using such kind of equations. Therefore, this work presents a rational version of homotopy perturbation method (RHPM) as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We present two case studies; for the first example, a comparison between the proposed method and the HPM method is presented; it will show how the RHPM generates highly accurate approximate solutions requiring less iteration, in comparison to results obtained by the HPM method. For the second example, which is a Van der Pol oscillator problem, we compare RHPM, HPM, and VIM, finding out that RHPM method generates the most accurate approximated solution.

Suggested Citation

  • Héctor Vázquez-Leal, 2012. "Rational Homotopy Perturbation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:490342
    DOI: 10.1155/2012/490342
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    References listed on IDEAS

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    1. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    2. Yasir Khan & Hector Vázquez-Leal & Luis Hernandez-Martínez, 2012. "Removal of Noise Oscillation Term Appearing in the Nonlinear Equation Solution," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, August.
    3. Yasir Khan & Hector Vázquez-Leal & Luis Hernandez-Martínez, 2012. "Removal of Noise Oscillation Term Appearing in the Nonlinear Equation Solution," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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