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An Improvement to the Homotopy Perturbation Method for Solving Nonlinear Duffing’s Equations

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Abstract

In this paper, a new form of the homotopy perturbation method has been adopted for solving nonlinear Duffing’s equations, which yields the Maclaurin series of the exact solution. The Laplace transformation is applied to the truncated Maclaurin series, and then the Padé approximation with fast convergence rate and high accuracy is used for the solution derived from the Laplace transformation. Illustrative examples are given to demonstrate the efficiency and the simplicity of the proposed method.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran

    A. R. Vahidi, E. Babolian & Z. Azimzadeh

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  1. A. R. Vahidi
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  2. E. Babolian
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  3. Z. Azimzadeh
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Correspondence to A. R. Vahidi.

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Communicated by Norhashidah Mohd. Ali.

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Vahidi, A.R., Babolian, E. & Azimzadeh, Z. An Improvement to the Homotopy Perturbation Method for Solving Nonlinear Duffing’s Equations. Bull. Malays. Math. Sci. Soc. 41, 1105–1117 (2018). https://doi.org/10.1007/s40840-015-0191-4

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  • DOI: https://doi.org/10.1007/s40840-015-0191-4

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