Residual Power Series Method and Adomian Decomposition Method for Solving Partial Differential Equations

Abstract

In This paper we present two methods, the first one is a powerful iterative method called Residual power series method introduced to obtain approximate solu­tions of nonlinear time-dependent generalized Fitzhugh-Nagumo equation with time-dependent coefficients and Sharma-Tasso-Olver equation subjected to certain initial conditions. In the second method we used Bernstein polynomials to modify the Adomian decomposition method which can be used to solve linear and nonlinear equations. Furthermore, the obtained results demonstrate reliability and activity of the proposed technique. Comparison with Other traditional technique