Analytical Solution of Liénard Differential Equation using Homotopy Perturbation Method

  • Md Mamun Ur Rashid Khan Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
  • Goutam Saha Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
Keywords: Homotopy Perturbation method (HPM); Liénard differential equation; Nonlinear differential equations; Analytic solution; Initial and boundary conditions

Abstract

In this research work, the well-known Homotopy perturbation method (HPM) is used to find the approximate solutions of the nonlinear Liénard differential equation (LDE) using different types of boundary conditions. In order to find the accuracy of the approximate solution, one term, two terms and three terms HPM approximations are considered. This idea is actually based on the idea of Taylor’s series polynomials. It is found that solution converges to the actual solution with the increase of the terms in the guess solution. Moreover, in each of the new HPM solution, previously obtained solutions are added to it in order to find the exactness of HPM solutions. However, the nature of the solution seems to be complicated. In addition, comparisons are made with the previously published results and a good agreement is observed.

GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 87-100

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Abstract
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Published
2019-11-19
How to Cite
Khan, M. M., & Saha, G. (2019). Analytical Solution of Liénard Differential Equation using Homotopy Perturbation Method. GANIT: Journal of Bangladesh Mathematical Society, 39, 87-100. https://doi.org/10.3329/ganit.v39i0.44160
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