A note on using the Differential Transformation Method for the Integro-Differential Equations

In this paper, we show that the generalization of the Differential Transformation Method (DTM) to Integro-Differential Equation is not the same thing that has been proposed in [P. Darania, A. Ebadian, A method for the numerical solution of the Integro-Differential Equation, Appl. Math. Comput. 188 (2007) 567-668]. We extend the integral part by the method of Jang et al. [2] for the Integro-Differential Equations. We give a counterexample for the method expressed by Darania and Ebadian [1] and some examples for comparing our modified method by method's of Darania and Ebadian [1].