Numerical study of the Sturm-Liouville problem

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 آذر 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.89575.1500

نویسندگان

Sergey Algazin¹؛ Artemiy Sinitsyn^{* 2}

¹Doctor 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

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

چکیده

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.

کلیدواژه‌ها

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