| Summary: | In this paper, we present a new simple and effective algorithm for solving generalized Pantograph equa-tions, delay differential equations with neutral terms and delay differential system with constant and variable coefficients.The new method is based on one of the Appell polynomials, namely Genocchi poly-nomials. We first introduce the properties of Genocchi polynomials and employed them to construct the operational matrices of derivative. Collocation method based on this operational matrix is used. Error estimate for this scheme based on the Generalized pantograph equations is reproduced. Only few terms of Genocchi polynomials are needed to obtain very good results. Numerical examples with comparison show the simplicity, efficiency and accuracy of the method.
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