An Efficient Variational Homotopy Transform Method for Solving Schrodinger Equation

Abstract

Abstract This paper presents a new methodology for solving Schrödinger equation based on the variational iteration method and the Kashuri-Fundo transform. The Lagrange multiplier is computed using the Kashuri - Fundo transform. This approach helps in avoiding the difficulties often appearing in finding Lagrange multiplier and the complicated integration used in Variational Iteration Method, as well as it does not need to use the convolution theorem of the transform. Furthermore, the Homotopy Perturbation Method is used to dealing with the nonlinear terms arising in the problems where the He’s polynomials are calculated. The proposed method emphasises the existence of the obtained solution in the absence of any linearization, discretization, or hypothesis. The suggested method’s compactness and reliability are demonstrated by numerical examples