On the numerical solution of generalized pantograph equation

In this study, a numerical algorithm for solving a generalization of a functional differential equation known as the pantograph equation is presented. Firstly, the proposed algorithm produces an approximate polynomial solution as a power series for the problem. Then, we transform the obtained power series into Padé series form to obtain an approximate polynomial of an arbitrary order for solving pantograph equation. The structure and advantages of using of the proposed method are presented. To show the validity and applicability of the numerical method some linear and nonlinear experiments are examined. The results reveal the high accuracy and efficiency of the proposed method.