Numerical study of the Sturm–Liouville problem

Document Type : Research Article

Authors

• S.D. Algazin ¹
• A.A. Sinitsyn ²

¹ Doctor 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,

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

10.22067/ijnao.2024.89575.1500

Abstract

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.

Keywords

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

Main Subjects

• Computational Mathematics

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References

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