Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials

Abstract

In this article we propose a numerical scheme to solve the pantograph equation. The method consists of expanding the required approximate solution as the elements of the shifted Chebyshev polynomials. The Chebyshev pantograph operational matrix is introduced. The operational matrices of pantograph, derivative and product are utilized to reduce the problem to a set of algebraic equations. An error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results.