Operational matrices of Chebyshev cardinal functions and their application for solving delay differential equations arising in electrodynamics with error estimation

In this paper, a new and effective direct method to determine the numerical solution of pantograph equation, pantograph equation with neutral term and Multiple-delay Volterra integral equation with large domain is proposed. The pantograph equation is a delay differential equation which arises in quite different fields of pure and applied mathematics, such as number theory, dynamical systems, probability, mechanics and electrodynamics. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. The operational matrices for the integration, product and delay of the Chebyshev cardinal functions are presented. A general procedure for forming these matrices is given. These matrices play an important role in modelling of problems. By using these operational matrices together, a pantograph equation can be transformed to a system of algebraic equations. An efficient error estimation for the Chebyshev cardinal method is also introduced. Some examples are given to demonstrate the validity and applicability of the method and a comparison is made with existing results.