Fredholm积分-微分方程的高精度数值方法研究
Research on high precision numerical method of Fredholm integro-differential equations
林楠 1张新东1
作者信息
- 1. 新疆师范大学数学科学学院,新疆乌鲁木齐 830017
- 折叠
摘要
研究积分项包含未知函数导数的Fredholm积分-微分方程的重心插值配点法.首先,利用重心Lagrange插值配点法和重心有理插值配点法构造Fredholm积分-微分方程的数值格式.其次,分别选取等距节点和第二类Chebyshev节点进行数值计算,并对两种插值法在不同节点下的精度进行比较.数值算例结果表明,两种插值配点法都可以得到较高的计算精度,但一般情况下为了得到高精度的数值解,优先采用重心Lagrange插值配点法在第二类Chebyshev节点上计算.
Abstract
In this paper,the barycentric interpolation collocation method for Fredholm integrodifferential equations whose integral term contains unknown function derivatives is studied.Firstly,the numerical scheme of Fredholm in-tegro-differential equations is constructed by using the barycentric Lagrange interpolation collocation method and barycentric rational interpolation collocation method.Secondly,the equidistant nodes and the second type of Cheby-shev nodes are selected for numerical calculation,and the accuracies of the two interpolation methods under different nodes are compared.The results of numerical examples show that the high computational accuracy can be obtained by the two interpolation collocation methods.However,in order to obtain high precision numerical solutions,we pre-fer to use the barycentric Lagrange interpolation collocation method on the second type of Chebyshev nodes.
关键词
Fredholm积分-微分方程/重心Lagrange插值/重心有理插值/Chebyshev节点/等距节点Key words
Fredholm integro-differential equation/barycentric Lagrange interpolation/barycentric rational inter-polation/Chebyshev node/equidistant node引用本文复制引用
基金项目
新疆维吾尔自治区自然科学基金杰出青年基金(2022D01E13)
国家自然科学基金(11861068)
新疆师范大学优秀青年科研启动基金(XJNU202012)
新疆师范大学优秀青年科研启动基金(XJNU202112)
出版年
2024
NETL
NSTL
万方数据