Newton-homotopy analysis method for nonlinear equations

In this paper, we present an efficient numerical algorithm for solving nonlinear algebraic equations based on Newton– Raphson method and homotopy analysis method. Also, we compare homotopy analysis method with Adomian’s decomposition method and homotopy perturbation method. Some numerical illustrations are given to show the efficiency of algorithm.

Newton–Raphson method; Homotopy analysis method; Adomian’s decomposition method; Homotopy perturbation method