APPLICATION OF LAPLACE TRANSFORM HOMOTOPY PERTURBATION METHOD TO NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

Prem Kiran G. Bhadane, V. H. Pradhan

Abstract: The Laplace transform is widely used to solve linear ordinary and partial differential equations. Recently many researchers have applied the Laplace transform (LT) with variational iteration method (VIM), Adomian decomposition method (ADM) and homotopy perturbation method (HPM) to obtain the solution of nonlinear differential equations. In the present paper the solution of some nonlinear differential equations are obtained on combining the Laplace transform with homotopy perturbation method (LTHPM). The present method detects the solution without any discretization or restrictive assumptions and therefore reduces the numerical computations to a greater extent. The obtained solutions are compared with the available exact solutions and the solutions obtained by homotopy perturbation method (HPM). It shows that the method LTHPM has a good agreement with the exact solution in comparison with HPM.

Keywords: Laplace Transform, Partial Differential Equation (PDE) and Laplace Transform with Homotopy Perturbation Method.

DOI: https://doi.org/10.15623/ijret.2016.0505077