Solving third-order nonlinear ordinary differential equation by adomian method

Abstract

ABSTRACT:
Numerous problems in Physics, Chemistry, Biology and Engineering science are modeled mathematically by systems of ordinary and fractional differential equations. Since most realistic differential equations do not have exact analytic solutions approximation and numerical techniques, therefore, are used extensively. Recently introduced Adomian Decomposition Method (ADM) [2] has been used for solving a wide range of problems. Adomian decomposition method has been known to be a powerful device for solving many functional equations as algebraic equations, ordinary and partial differential equations, integral equations and so on. It is demonstrated that this method has the ability of solving systems of both linear and non-linear differential equations: it yields analytical solutions and offers certain advantages over standard numerical methods. It is free from rounding off errors since it does not involve discretization, and is computationally inexpensive.
In this paper, we used the revised Adomian decomposition method for solving third-order nonlinear ordinary differential equation. It demonstrated that the series solution thus obtained converges faster relative to the series obtained by standard ADM. Several illustrative examples have been presented

Keywords: differential equation, nonlinear, third-order, Adomian