Numerical study of the Sturm-Liouville problem

Articles in Press

Document Type : Research Article

Authors

• Sergey Algazin ¹
• Artemiy Sinitsyn ²

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

² Department of Elasticity Theory, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia.

10.22067/ijnao.2024.89575.1500

Abstract

There are a number of competing methods for the numerical solution of the eigenvalue problem. These are, first of all,
projection methods: the Ritz method, the Bubnov-Galerkin method, etc. We know quite a lot about the accuracy provided
by these methods. For example, the approximations for the eigenvalues of self-adjoint problems given by the Ritz method
lie on top of the exact values. A number of convergence results are known, and in some special cases error estimates of
projection methods are obtained.

Keywords

• Sturm-Liouville problem
• Numerical algorithm without saturation
• Computational experiment

Main Subjects

• Computational Mathematics

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