Numerical solution of Volterra integro-differential equations by superimplicit multistep collocation methods

Abstract

In this paper, we introduce a new family of extended multistep collocation methods for solving two types of nonlinear Volterra integro-differential equations including nonstiff and stiff problems. These methods are constructed by using super-future points technique with the aim of increasing the order and the stability region of the classical one-step collocation methods and multistep collocation methods without increasing the computational cost. We analyze the convergence order of the constructed methods and their linear stability properties. Numerical experiments confirm the theoretical expectations.