摘要
文章提出了求解Volterra积分方程的一种高精度数值方法:重心插值配点法(包括重心Lagrange插值配点法和重心有理插值配点法)。该方法分为两步:首先对Volterra积分方程采用两种重心插值配点法进行离散,构造出Volterra积分方程的数值求解格式;然后,依次选取第二类Chebyshev节点和等距节点进行数值计算。文章主要研究积分项中含有未知函数的一阶导函数的Volterra积分方程的离散格式构造及数值实现。数值实验结果表明:在使用第二类Chebyshev节点时,用重心Lagrange插值配点法较好;在使用等距节点时,使用重心有理插值配点法较好。
In this paper,a high precision numerical method is introduced for solving Volterra integral equation.That is Barycentric Interpolation Collocation Method(Barycentric Lagrange Interpolation Collocation Method(BLICM)and Barycentric Rational Interpolation Collocation Method(BRICM)).There are two steps in the method.Firstly,the Volterra integral equation is discretized by barycentric interpolation collocation method,and then the numerical scheme of Volterra integral equation will be obtained.Secondly,the second type of Chebyshev nodes and equidistant nodes are selected for numerical calculation.In this paper,the discrete scheme and numerical implementation of Volterra integral equation with the first derivative of unknown function are studied.The numerical results show that when the second kind of Chebyshev nodes are used,the results of BLICM is better than ones of BRICM,however,when the equidistant nodes are used,the results of BRICM is better than ones of BLICM.
作者
于孟文
张新东
YU Meng-wen;ZHANG Xin-dong(School of Mathematical Sciences,Xinjiang Normal University,Urumqi,Xinjiang,830017,China)
出处
《新疆师范大学学报（自然科学版）》
2023年第1期75-80,共6页
Journal of Xinjiang Normal University(Natural Sciences Edition)
基金
国家自然科学基金(11861068)
新疆维吾尔自治区自然科学基金——杰出青年基金项目(2022D01E13)
新疆师范大学优秀青年科研启动基金(XJNU202012,XJNU202112)。
