Homotopy Perturbation Based Galerkin Method for Solving Linear and Non-Linear Ordinary Differential Equations over Semi-Infinite Domain

This paper proposes an improved version of the Homotopy Perturbation Method (HPM) that is specifically designed to solve a wide range of boundary value problems (BVPs), including both linear and nonlinear differential equations over a semi-infinite domain. Although HPM in its classical sense is capable of solving a large number of BVPs, but there are certain shortcomings when it comes to the problems defined over semi-infinite domains. We have highlighted some of these cases in this manuscript by studying suitable examples. On the other hand, the solutions to nonlinear problems using HPM are too lengthy to be displayed, or to be readily reused. To overcome these shortcomings, we have combined HPM with another scheme, namely Galerkin Method, and propose a hybrid of both, which may be referred to as Homotopy Perturbation Based Galerkin Method (HPGM). We have demonstrated the accuracy of the newly proposed method by comparing it with the exact solutions of some benchmark problems. We have found an excellent agreement between the solutions, and furthermore, the accuracy of the proposed technique is improved and also shown by plotting the residual error functions.