第二类非线性Fredholm型积分方程数值解的超收敛性

本文讨论第二类非线性Ｆｒｅｄｈｏｌｍ型积分方程数值解的超收敛性，以Ｇａｌｅｒｋｉｎ方法为基础建立了该类方程的Ｇａｌｅｒｋｉｎ算法、小波Ｇａｌｅｒｋｉｎ算法以及它们相应的迭代校正格式，证明了两种算法数值解的超收敛性，不仅将Ｈａｍｍｅｒｓｔｅｉｎ积分方程的结果推广到第二类非线性Ｆｒｅｄｈｏｌｍ型积分方程，而且应用小波分析工具得到了更精确的结果．

Superconvergence of Numerical Solutions to Nonlinear Fredholm Equations of the Second Kind

This paper discusses the superconvergence of numerical solutions to the nonlinear Fredholm integral equations of the second kind. On the basis of Galerkin Method, the auther has established Galerkin algorithm, Wavelet Galerkin algorithm and their corresponding iterated check schemes for this kind of equations.The superconvergence of the numerical solutions of these two algorithm has been proved. No only have the results concerning Hammerstein integral equations been generalized to the second kind of nonlinear Fredholm integral equations, but also more precise results have been obtained by using Wavelet analytical method.