Multistep collocation methods for Volterra integro-differential equations

摘要

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 A0-stable methods are provided. Numerical experiments confirm theoretical expectations and make comparisons with the one-step collocation methods.