一类非线性积分方程的分段多项式配置解及其迭代配置解

The Solutions of A Class of Nonlinear Integral Equations By Piecewise Polynomial Collocation And Its Iterated Collocation Methods

§1.引言 分段多项式配置及其迭代配置方法(以下简称配置方法)以其计算简单、超收敛性等特点在积分方程的数值分析中倍受重视.本文考虑如下一类非线性积分方程:其中,y,φ∈L_∞(I),?_t∈I,k_t(t,s)∈L_1(I).Chandrasekhar H-积分方程是(1.1)的特殊情形,对迁移理论很重要.

In this paper, the application of piecewise polynomial spline collocation and itsiterated Collocation methods to a class of nonlinear integral equations: y(t)=?(t)+y(t)∫from 0 to 1 k(t, s)y(s)ds, including Chandrasekhar H-equations as a special case,is stud-ied. It is shown that the collocation solution leads to local superconvergence at knotsof the approximating function, while the iterated collocation solution yields globalsuperconvergence on the entire interval of integration. A numerical example is given.