Numerical Solutions for Nonlinear Fredholm Integral Equations of the Second Kind and Their Superconvergence

摘要

This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of the second kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkin algorithm and their corresponding iterated correction schemes for this kind of equations. The superconvergernce of the numerical solutions of these two algorithms is proved. Not only are the results concerning the Hammerstein integral equations generalized to nonlinear Fredliolm equations of the second kind, but also more precise results are obtained by using the wavelet method.