Extrapolation of Nystrom Solution for Two-Dimensional Nonlinear Fredholm Integral Equations

In this paper, we analyze the existence of asymptotic error expansion of Nystrom solution for two-dimensional nonlinear Fredholm integral of the second kind. We show that the Nystrom solution admits an error expansion in powers of the step-size h and the step-size k. For a special choice of the numerical quadrature, the leading terms in the error expansion for the Nystrom solution contain only even powers of h and k, beginning with terms h^2p and k^2q. These expansions are useful for the application of Richardson extrapolation and for obtaining sharper error bounds. Numerical examples show that how Richardson extrapolation gives a remarkable increase of precision, in addition to faster convergence.