Implementation to the different differential equations of homotopy analysis and comparison with differential transformed, adomian decomposition method

In this study, the concept of Homotopy Analysis Method (HAM), 'Transformed Differential Method (DTM)' and 'Adomian Decomposition Method (ADM)' are introduced. Furthermore some non-lineer 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. Additionaly, 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 solution of two examples are presented and the results are shown in tables and figures.