首页|Fredholm积分-微分方程的高精度数值方法研究

Fredholm积分-微分方程的高精度数值方法研究

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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。
Research on high precision numerical method of Fredholm integro-differential equations
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.

Fredholm integro-differential equationbarycentric Lagrange interpolationbarycentric rational inter-polationChebyshev nodeequidistant node

林楠、张新东

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新疆师范大学数学科学学院,新疆乌鲁木齐 830017

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

新疆维吾尔自治区自然科学基金杰出青年基金国家自然科学基金新疆师范大学优秀青年科研启动基金新疆师范大学优秀青年科研启动基金

2022D01E1311861068XJNU202012XJNU202112

2024

商丘师范学院学报
商丘师范学院

商丘师范学院学报

CHSSCD
影响因子：0.211
ISSN：1672-3600
年,卷(期)：2024.40(3)
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