Operational matrix based on Genocchi polynomials for solution of delay differential equations

Abstract

In this paper, we present a new simple and effective algorithm for solving generalized Pantograph equations, 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 polynomials. 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. Keywords: Genocchi polynomials, Operational matrix of derivatives, Generalized pantograph equations, Delay differential equations, Collocation points