A parallel fifth-order algorithm for the numerical solution of Volterra equations

An iterative algorithm based upon the use of a nonpurely polynomial extension of the standard Newton-Cotesʹ quadrature rules is constructed to yield the numerical solution of Volterra-type integral equations (with nonsingular kernel) with an accuracy of fifth order in the distance between grid points. This algorithm which is easily parallelizable for a small number of processors, is illustrated and analysed by means of three test equations.