Nonlinear Integro-differential Equations by Differential Transform Method with Adomian Polynomials

Abstract

A modification of differential transformation method is applied to nonlinear integro- differential equations. In this technique, the nonlinear term is replaced by its Adomian polynomials for the index k, and hence the dependent variable components are replaced in the recurrence relation by their corresponding differential transform components of the same index. Thus the nonlinear integro- differential equation can be easily solved with less computational work for any analytic nonlinearity due to the properties and available algorithms of the Adomian polynomials. New theorems for products and integrals with nonlinear functions are introduced. Several illustrative examples with different types of nonlinearities are considered to indicate the effectiveness of the present technique.