On the coupling of the homotopy perturbation method and Laplace transformation

In this paper, a Laplace Homotopy perturbation method is employed for solving onedimensional non-homogeneous partial differential equation with a variable coefficient. This method is a combination of the Laplace transform and Homotopy Perturbation Method (LHPM). LHPM presents an accurate methodology to solve non-homogeneous partial differential equation with variable coefficient. The aim of using the Laplace transform is to overcome the deficiency that mainly caused by unsatisfied conditions in other semi-analytical methods such as HPM, VIM, and ADM. The approximate solutions obtained by means of LHPM in a wide range of problem’s domain were compared with those results obtained from the actual solutions, Homotopy perturbation method (HPM) and the finite element method. The comparison shows a precise agreement between the results, and introduces this new method as an applicable one which it needs less computations and is much easier and more convenient than others, so it can be widely used in engineering too. * b Corresponding Author: [email protected] (Yasir Khan) *Manuscript Click here to view linked References