一类带比例时滞Fredholm型积分方程Legendre配置解法及收敛性分析

Legendre-Collocation Method and Convergence Analysis for a Kind of Fredholm Integral Equation with Proportional Delay

本文利用Legendre配置方法探讨一类带比例时滞Fredholm型积分方程的数值解法.首先利用Gauss-Legendre求积公式将积分项进行离散,然后将Legendre多项式的零点取为离散化方程组的配置点,把积分方程转化为代数方程组后进行求解,并给出了数值求解格式和收敛性定理,最后列举若干数值例子以验证该方法的有效性与可靠性.

In this paper, the Legendre-Collocation method is presented for numerically solving the Fredholm integral equation with proportional delay. First, taking some collocation points, the integral equation is translated into algebraic equation. By adopting the Gauss-Legendre integral formula, let the zeros of Legendre polynomials be the collocation points, the integral equation is discreted to algebraic equations. Secondly, the format of numerical solution and convergence theorem are obtained by the Legendre-Collocation method and some numerical examples are given to illustrate the accuracy and dependability of the method.