The homotopy analysis Rangaig transform method for nonlinear partial differential equations

Abstract

The idea suggested in this article is to combine the Rangaig transform with the homotopy analysis method in order to facilitate the solution of nonlinear partial differential equations. This method may be called the homotopy analysis Rangaig transform method (HARTM). The proposed example results showed that HARTM is an effective method for solving nonlinear partial differential equations.

Numerical scheme methods for solving nonlinear pseudo-hyperbolic partial differential equations

“…In recent years, many authors have been interested in testing partial differential equations using different numerical and analytical methods, among these are the Adomian decomposition method [1], the homotopy perturbation method [2], the multiple Exp-function method [3], the Homotopy analysis Rangaig transform method [4] the finite difference method [5,6], the variational iteration method [7], the residual power series method [8], the He's variational iteration method [9] and the homotopy analysis method [10] have been applied to solve linear and nonlinear partial differential equations.…”