The Numerical Solution of an Abelian Ordinary Differential Equation by a New Hybrid of ADM and Its Comparism with some Standard Numerical Scheme

Abstract

In this paper we present a relatively new technique call theNew Hybrid of Adomian decomposition method (ADM) for solution of an Abelian Differential equation. The numerical results of the equation have been obtained in terms of convergent series with easily computable component. These methods are applied to solve some problem represented as Abelian differential equation and the current results compared with an established Runge-kutta of order IV in order to verify the accuracy and also with Actual solution. This findings confirm that some know methods and the New Hybrid are powerful and efficient tools for solving Abelian differential equation.

Keywords: Abelian differential equation, Adomian decomposition method, Runge-kutta of order IV, New hybrid ADM.