Homotopy analysis method and how the choice of base functions affect the convergence of homotopy series solution.

In this study, we will understand the concept and procedure of Homotopy Analysis Method(HAM), which is a strong semi analytic method to solve highly nonlinear integral, differential equations. This method provides a lot of freedom to control the convergence of the solution so obtained by this method. Here we will see one such aspect, the freedom to choose the Base Function, in approximating the actual solution and how the choice affects the rate of convergence of the approximate series solution. [ABSTRACT FROM AUTHOR]