An implicit method for the numerical solution of Volterra integro-differential equations

(In this paper, we consider an implicit Continuous Block Backward Differentiation formula (CBBDF for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability region of orders 2, 3 and 4 are constructed which are suitable for solving stiff problems.