Chebyshev Collocation Methods for Volterra Integro-differential Equations of Pantograph Type

A numerical scheme based upon the Chebyshev polynomials and collocation method is modified and developed to deal with a class of Volterra integro-differential equations. First, we construct the operational matrices of derivative and pantograph. Then these obtained matrices are then utilized to convert the problems to a system of algebraic equations. Furthermore, we establish a detailed convergence analysis in the weighted square norm. Finally, three numerical experiments are implemented and discussed to confirm the applicability and accuracy of the introduced computational scheme.