Approximation of Functional-Algebraic Eigenvalue Problems

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-09-11 DOI:10.1134/s0012266124050100

D. M. Korosteleva

引用次数: 0

Abstract

We propose a new symmetric variational functional-algebraic statement of the eigenvalue problem in a Hilbert space with a linear dependence on the spectral parameter for a class of mathematical models of thin-walled structures with an attached oscillator. The existence of eigenvalues and eigenvectors is established. A new symmetric approximation of the problem in a finite-dimensional subspace with a linear dependence on the spectral parameter is constructed. Error estimates are obtained for the approximate eigenvalues and eigenvectors. The theoretical results are illustrated with an example of a structural mechanics problem.

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函数代数特征值问题的近似方法

摘要我们针对一类带有附加振荡器的薄壁结构数学模型，提出了一种新的对称变分函数代数陈述，即在希尔伯特空间中，特征值问题与谱参数线性相关。确定了特征值和特征向量的存在。构建了该问题在有限维子空间中的新对称近似值，该近似值与谱参数成线性关系，并获得了近似特征值和特征向量的误差估计。以一个结构力学问题为例对理论结果进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.