Adomian Decomposition Method for direct integration of Bernoulli differential equations

Abstract

We introduce the basic and less known methodology of Adomian Decomposition Method (ADM) that yields series solutions for differential equations. We then formulate the method to obtain analytic solutions, in a rapidly convergent series, to some class of higher order differential equations. ADM is a type of algorithm applicable to various ordinary or partial differential equations including Bernoulli Differential Equations (BDEs) as proved by the present paper. The results show excellent potentials of applying this method.