Gq. Han, ASYMPTOTIC ERROR EXPANSION OF A COLLOCATION-TYPE METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL-EQUATIONS, Applied numerical mathematics, 13(5), 1993, pp. 357-369
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.