Efficient general linear methods for a class of Volterra integro-differential equations

This paper concerns on the introduction of a method for solving a class of Volterra integro-differential equations (VIDEs) of the second kind. It is based on the combination of special general linear methods for ordinary differential equations and Gregory quadrature rule and equipped with a starting procedure. The convergence and stability of the method are analyzed. Some numerical experiments are given to illustrate the agreement of our implementation with the theoretical convergence orders and show the capability of the method in solving nonlinear VIDEs.