基于Bernstein多项式求解Fredholm积分方程的离散化方法  

Discretization Method of Solving 2D Fredholm Integral Equations Based on Bernstein Polynomial

作　　者：潘超 陈豫眉 PAN Chao;CHEN Yumei(College of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China;College of Mathematics Education,China West Normal University,Nanchong Sichuan 637009,China;Institute of Computing Method and Application Software,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009 [3]西华师范大学计算方法及应用软件研究所,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2021年第3期254-259,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金面上项目(11971094);四川省科技厅项目(2017JY0186);西华师范大学英才基金项目(17YC371)。

摘　　要：本文运用一种离散化方法求解二维第二类Fredholm积分方程。该方法首先利用Bernstein多项式基函数代替二维第二类Fredholm积分方程中的未知函数,其次将积分方程转化为线性方程组,最后求出数值解。实验表明,该方法具有很好的收敛性,该数值解与理论相符。A discretization method is employed in this paper to solve 2D Fredholm integral equations of second kind.Firstly,the unknown function of 2D Fredholm integral equations of second kind is replaced with Bernstein polynomial basis functions.Secondly,the integral equation is transformed into the system of linear equations.Finally,the numerical solution is obtained.The experiment shows that this method is of good convergence and the results of experiment correspond to the theory.

关 键 词：离散化 FREDHOLM积分方程 收敛性分析 BERNSTEIN多项式 误差分析 

分 类 号：O241.83[理学—计算数学]