Shehu Transform Homotopy Analysis Method for the Solution of Nonlinear Initial Value Ordinary and Partial Differential Equations

Abstract

In this paper, we propose a method of solution for both nonlinear Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs). Shehu Transform is combined with Homotopy Analysis Method (HAM) to handle both homogeneous and nonhomogeneous problems in the family of differential equations considered. The properties of homotopy derivatives are exploited while handling the nonlinear terms encountered. Several examples are solved using HAM and the Shehu Transform Homotopy Analysis Method (STHAM) proposed in this work, and the effectiveness of the proposed method is obvious in terms of reduction in the volume of computations and time. All computations are carried out with the aid of Mathematica 12.0.