基于Legrndre小波的第一类Fredholm积分方程的数值解法研究  

Numerical Research of Fredholm Integral Equations of the First Kind Based on the Legendre Wavelets

作　　者：董媛媛 陈蕾 DONG Yuan-yuan;CHEN Lei(Department of Maths and Finance,Hanjiang Normal University,Shiyan 442000,China;Qiongtai Normal-University,Haikou 570100,China)

机构地区：[1]汉江师范学院数学与财经系,湖北十堰442000 [2]琼台师范学院,海南海口570100

出　　处：《数学的实践与认识》2019年第1期241-246,共6页Mathematics in Practice and Theory

基　　金：湖北省教育厅项目:"代数K-理论与同调代数及其应用"(T201731);湖北省教育厅项目<基于博弈论的环境敏感区绿色绩效评价体系构建研究-以南水北调中线工程水源区为例>(18Q189)

摘　　要：提出利用Legendre小波函数去获得第一类Fredholm积分方程的数值解,函数定义在区间[0,1)上,然后结合Garlerkin方法将原问题转化为线性代数方程组.而且还对算法的收敛性和误差进行了分析,最后通过两个数值算例验证了所提算法的可行性及有效性.In this paper, a numerical scheme for solving Fredholm integral equations of the first kind via Legendre wavelet has been proposed, this method is based on the orthogonal functions on[0, 1)combined with Galerkin method, then the original problem is transformed into a system of linear algebraic equations. In addition the convergence and error are investigated. Lastly two numerical examples have been presented to test the effectiveness and feasibility of the proposed method.

关 键 词：LEGENDRE小波 FREDHOLM积分方程 数值解 GALERKIN方法 

分 类 号：O241.83[理学—计算数学]