Homotopy Analysis Method

Abstract

Homotopy analysis method (HAM) is one of the well‐known semi‐analytical methods for solving various types of linear and nonlinear differential equations (ordinary as well as partial). This method is based on coupling of the traditional perturbation method and homotopy in topology. By this method one may get exact solution or a power series solution which converges in general to exact solution. The HAM consists of convergence control parameter, which controls the convergent region and rate of convergence of the series solution. This chapter applies the present method to solve a linear partial differential equation in a numerical example and a nonlinear partial differential equation in another numerical example. It may be noted that the HAM not only produces approximate convergent series solution but it can also give exact solution depending on the considered problem with proper control parameter.