A parallel fifth-order algorithm for the numerical solution of Volterra equations (Q1919944)

For the numerical solution of second-kind Volterra integral equations the authors consider a modification of a standard approach, which consists in replacing the weights for Simpson's rule and for the trapezoidal rule by modified Newton-Cotes quadratures involving one free parameter. A suitable choice of this parameter increases the order, but makes the method implicit. It is shown that in a parallel environment (with, say, 4 processors) the new algorithm can be executed in about the same time as the standard method.