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

摘要

A numerical scheme based upon the Chebyshevpolynomials and collocation method is modified and developedto deal with a class of Volterra integro-differential equations.First, we construct the operational matrices of derivative andpantograph. Then these obtained matrices are then utilizedto convert the problems to a system of algebraic equations.Furthermore, we establish a detailed convergence analysis inthe weighted square norm. Finally, three numerical experimentsare implemented and discussed to confirm the applicability andaccuracy of the introduced computational scheme.