ASYMPTOTIC ERROR EXPANSION OF A COLLOCATION-TYPE METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL-EQUATIONS

Recently, Kumar and Sloan introduced a new collocation-type method for the numerical solution of Fredholm-Hammerstein integral equations. Br unner applied this method to nonlinear Volterra integral and integro-d ifferential equations and discussed its connection with the iterated c ollocation method. In the present paper, the asymptotic error expansio n of this method for nonlinear Volterra integral equations at mesh poi nts is obtained. We show that when piecewise polynomials of PI(p-1) ar e used, the approximate solution admits an error expansion in powers o f the stepsize h, beginning with a term h(p). For a special choice of the collocation points, the leading terms in the error expansion for t he collocation solution contain only even powers of the stepsize h, be ginning with a term h2p. Thus Richardson's extrapolation can be perfor med on the solution; and this will greatly increase the accuracy of th e numerical solution.