Multistep collocation methods for Volterra integro-differential equations

Keywords: Volterra integro-differential equations Multistep collocation Superconvergence Stability a b s t r a c t Multistep collocation methods for Volterra integro-differential equations are derived and analyzed. They increase the order of convergence of classical one-step collocation methods, at the same computational cost. The numerical stability analysis is carried out and classes of A 0-stable methods are provided. Numerical experiments confirm theoretical expectations and make comparisons with the one-step collocation methods.