A New and Reliable Modification of Homotopy Perturbation Method

Abstract

This manuscript introduces a new alteration to the Homotopy Perturbation Method by coupling it with the Laplace Transform. The corresponding Homotopy Perturbation Laplace Method (HPLM) promises better results in terms of accuracy, efficiency, and easy-of-use when compared to other semi-numerical schemes, and is therefore conveniently poised to be used for various problems in science and engineering. The method is tested against standard fifth and sixth order linear and nonlinear ordinary differential equations. For validity, the obtained results are compared with well known analytical and numerical schemes.