Solving Non-linear Partial Differential Equations Using Homotopy Analysis Method (HAM)

Abstract

AbstractIn this research paper, a semi-analytical method,i.e.,homotopy analysis method, is implemented for finding the solution of non-linear partial differential equations. Homotopy analysis method is very effective, and easy to evaluate as compared to other numerical methods. The results through HAM on illustrative examples are compared with two well-known methods, namely, Variational Iteration Method(VIM) and Adomian Decomposition Method(ADM). The comparisons of obtained solutions results in the high accuracy through HAM when compared to the other competing methods. Hence, the solution obtained using HAM has much faster convergence to the exact solution.KeywordsNon-linear partial differential equationNumerical resultsHomotopy analysis method