基于分片线性最大Rényi熵的Fredholm积分方程数值解法  

Numerical solution of Fredholm integral equations via piecewise linear maximum Rényi entropy method

作　　者：管钰 丁玖 靳聪明[1] GUAN Yu;DING Jiu;JIN Congming(School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China;Department of Mathematics,The University of Southern Mississippi,Hattiesburg,MS 39406-5045,USA)

机构地区：[1]浙江理工大学理学院,杭州310018 [2]南密西西比大学数学系,美国密西西比州哈蒂斯堡39406-5045

出　　处：《浙江理工大学学报（自然科学版）》2022年第6期950-958,共9页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(11571314)。

摘　　要：大部分积分方程无法求出精确解,因此需考虑数值方法得到近似解。提出了一种基于分片线性基函数的最大Rényi熵的函数恢复方法,证明了解的唯一性,并在此基础上给出基于分片线性最大Rényi熵的Fredholm积分方程数值解法。数值实验表明:基于分片线性最大Rényi熵的Fredholm积分方程数值解法有效,且可以得到比基于分片线性最大Shannon熵的数值解法精度更高的解。The exact solutions cannot be found for most integral equations, so numerical methods should be considered to obtain the approximate solutions. In this paper, a maximum Rényi entropy method based on piecewise linear basis functions is proposed to recovery the functions. The uniqueness of the solution of this piecewise linear maximum Rényi entropy method is proved. Then it is used to solve the Fredholm integral equations. Numerical experiments show that the proposed piecewise linear maximum Rényi entropy method for solving the Fredholm integral equations is efficient, and can obtain better solutions than those of the piecewise linear maximum Shannon entropy method.

关 键 词：最大熵原理 Rényi熵 分片线性基函数 FREDHOLM积分方程 数值解法 

分 类 号：TS195.644[轻工技术与工程—纺织化学与染整工程]