A multistep collocation method for approximate solution of Volterra integro-differential equations of the third kind

In this paper, we use the multistep collocation method for linear Volterra integro-differential equations of the third kind. First, the structure of multistep collocation method is described, then the convergence of the method and its order are investigated. The comparison of the proposed method with classical one-step collocation method shows that the order of convergence increases with the same computational cost. Some numerical examples are given in the last part of the article to illustrate the theoretical results.