Nonlinear Differential and Integro-Differential Equations with Proportional Delays by Differential Transform Method with Adomian Polynomials

In this paper, the differential transformation is applied to approximate and exact solutions of nonlinear integro-differential and differential equations with proportional delays. In this technique, the nonlinear term is replaced by its Adomian polynomials for k index, so the dependent variable components in the recurrence relation are replaced by their corresponding differential transform components of the same index. Therefore, the nonlinear integro-differential equation can be easily solved with less computational works for any analytical nonlinearity due to the available algorithms and properties of the Adomian polynomials. In illustrative examples, the present method is applied to a few types of nonlinearity are treated and the proposed technique has provided good results.