Modified multilag methods for Volterra functional equations

Linear multistep methods for ordinary differential equations in conjunction with a family of computationally efficient quadrature rules are employed to define a class of so-called multilag methods for the solution of Volterra integral and integro-differential equations. In addition, modified multilag methods are proposed which have the property that the stability behavior is independent of the choice of the quadrature rules. High order convergence of the methods is established. In particular, a special class of high order convergent methods is presented for the efficient solution of first-kind Volterra equations. Numerical experiments are reported.