Numerical study of the Sturm–Liouville problem

Iranian Journal of Numerical Analysis and Optimization

مقاله 9، دوره 15، Issue 2 - شماره پیاپی 33، تابستان 2025، صفحه 645-654   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.89575.1500

نویسندگان

S.D. Algazin¹؛ A.A. Sinitsyn^{* 2}

¹Doctor of Physical and Mathematical Sciences, Leading Researcher, Laboratory of Me- chanics and Optimization of Structures, Ishlinsky Institute for Problems of Mechanics of the Russian Academy of Sciences,

²Student of the MSU Faculty of Mechanics and Mathematics, Department of Elasticity Theory,

چکیده

The article discusses the general Sturm–Liouville problem. To solve it numerically, a new algorithm is proposed, which is based on the varia-tional principle and does not use saturation. The problem of constructing numerical methods for solving eigenvalue problems can be divided into two stages. First, we need to reduce the infinite-dimensional problem into a finite-dimensional one, and then find a method for solving this finite-dimensional algebraic eigenvalue problem. In this paper, we only consider the first stage, and solve the resulting algebraic problem using the QR al-gorithm. A comparison with the results of other authors is also carried out. Methodical calculations confirm the correctness of the new approach.

کلیدواژه‌ها

Sturm–Liouville problem؛ Numerical algorithm without satura-tion؛ Computational experiment

مراجع