Implementation to the Different Differential Equations of Homotopy Analysis, Differential Transformed and Adomian Decomposition Method

Abstract

In this study, the concept of Homotopy analysis method (HAM) is briefly introduced. Furthermore some non-linear problems are handled and the solutions of these problems are given using by HAM, DTM, ADM methods and the convergence of the solution is shown to the exact solution. Additionally, the three methods are compared and it is observed that the HAM is more-less efficient and effective than the ADM and DTM in according to the exact solution. In the end, some of the numerical solutions of two examples are presented and the results are shown in graphs and figures.