Numerical algorithms for recovering a fractional Sturm-Liouville operator based on trace formulae

IF 1.7 3区 数学 Q2 MATHEMATICS, APPLIED Numerical Algorithms Pub Date : 2024-09-07 DOI:10.1007/s11075-024-01926-5
Xiaowen Li, Xiaoying Jiang, Xiang Xu
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Abstract

This paper explores numerical methods for recovering a density term in a fractional Sturm-Liouville problem using a set of spectra. By applying Lidskii’s theorem, a sequence of trace formulae are derived to elucidate the connections between the unknown coefficients and the complex eigenvalues of a fractional spectra problem. Two efficient algorithms are proposed based on these trace formulae, and their effectiveness is demonstrated through numerical experiments.

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基于迹公式的分数斯特姆-利乌维尔算子恢复数值算法
本文探讨了利用一组谱恢复分数 Sturm-Liouville 问题中的密度项的数值方法。通过应用 Lidskii 定理,推导出一系列迹公式,以阐明未知系数与分数谱问题复特征值之间的联系。根据这些迹公式提出了两种高效算法,并通过数值实验证明了它们的有效性。
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来源期刊
Numerical Algorithms
Numerical Algorithms 数学-应用数学
CiteScore
4.00
自引率
9.50%
发文量
201
审稿时长
9 months
期刊介绍: The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.
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