Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method |
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Authors: | Yusry O. El-Dib Nasser S. Elgazery |
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Affiliation: | Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt |
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Abstract: | In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the first-order solvability condition. The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science. |
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Keywords: | Damped Mathieu Equation parametric nonlinear oscillator resonance instability homotopy perturbation method (HPM) |
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