Multistep collocation approximations to solutions of first-kind Volterra integral equations

The multistep collocation method is applied to Volterra integral equations of the first kind. The existence and uniqueness of the multistep collocation solution are proved. Then the convergence condition of the multistep collocation method is analyzed and the corresponding convergence order is described. In particular, for cm=1, the convergence conditions, which can be easily implemented, are given for two-step and three-step collocation methods. Numerical experiments illustrate the theoretical analysis.