A GLMs-based difference-quadrature scheme for Volterra integro-differential equations

Abstract

In this paper, a class of general linear methods is combined with a special quadrature rule inherited from natural Runge–Kutta methods for Volterra integral equations to design a more stable and efficient algorithm. The constructed methods of orders 1,2, and 3 are A0–stable and the method of order 4 is A0(α)–stable. The capability of the proposed methods in solving stiff and nonstiff problems is shown by some numerical experiments.