一类Fredholm积分–微分方程的重心Jacobi插值求解法
Barycentric Jacobi Interpolation Method for Solving a Kind of Fredholm Integral-Differential Equation
DOI: 10.12677/pm.2024.144142, PDF,    科研立项经费支持
作者: 刘高原, 张 益：西华师范大学数学与信息学院，四川 南充；陈 冲：西华师范大学公共数学学院，四川 南充
关键词: 重心Jacobi插值配置法；Fredholm积分–微分方程；误差估计；Barycentric Jacobi Interpolation Collocation Method； Fredholm Integral-Differential Equation； Error Estimates
摘要: 本文运用重心Jacobi插值配置法求解一类Fredholm积分–微分方程。首先通过取消重心Gegenbauer插值中参数相等的条件，得到重心Gegenbauer插值的一般形式——重心Jacobi插值，并表明重心Jacobi插值等价于插值节点为移位Gauss-Jacobi节点的Jacobi插值。然后基于配置法，应用重心Jacobi插值构造一类带有初值条件的Fredholm积分–微分方程的数值算法。误差估计表明，在合适的条件下，该算法是收敛的。最后，数值算例验证算法的有效性。
Abstract: In this paper, the barycentric Jacobi interpolation collocation method is used to solve a kind of Fredholm Integral-Differential equation. Firstly, the general form of barycentric Gegenbauer interpolation, barycentric Jacobi interpolation, is obtained by canceling the condition that the parameters in barycentric Gegenbauer interpolation are equal, and it is shown that the barycentric Jacobi interpolation is equivalent to the Jacobi interpolation whose interpolation nodes are shifted Gauss-Jacobi nodes. Then based on the collocation method, the numerical algorithm for a kind of Fredholm Integral-Differential equation with initial value conditions is constructed by barycentric Jacobi interpolation. The result of error estimates show that the algorithm is convergent under suitable conditions. Finally, the effectiveness of the algorithm is verified by a numerical example.
文章引用：刘高原, 张益, 陈冲. 一类Fredholm积分–微分方程的重心Jacobi插值求解法[J]. 理论数学, 2024, 14(4): 342-354. https://doi.org/10.12677/pm.2024.144142

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