Homotopy Perturbation Transform Method for solving nonlinear wave-like equation with variable coefficients

Abstract

In this paper, we apply homotopy perturbation transform method (HPTM) for solving nonlinear wave-like equations of variable coefficients. This method is the coupling of homotopy perturbation method and Laplace transform method. The nonlinear terms can be easily obtained by the use of He’s polynomials. HPTM present an accurate methodology to solve many types of linear and nonlinear differential equations. The approximate solutions obtained by means of HPTM in a wide range of the problem’s domain were compared with those results obtained from the actual solutions, the Variational iteration method (VIM) and the Adomain decomposition method (ADM). The fact that proposed technique solves nonlinear problems without using Adomain’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method. The comparison shows a precise agreement between the results.

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March 10, 2026

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