Computing the sums of Rayleigh-Schrödinger series of perturbed self-adjoint operators

Кадченко, С.И.

doi:10.1134/s0965542507090059

Cited by 6 publications

(4 citation statements)

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“…The method is based on the Bubnov-Galerkin scheme as applied to the eigenvalue problem , (2.41) which can be written as . (2.43) An approximate solution of problem (2.40) is sought in the form of the sum where are the eigenvalues of T, which form a basis in H. This method is justified in detail in [25]. Next, these general results are applied to the eigenvalue problem for the Orr-Sommerfeld operator in the case of a viscous incompressible plane parallel flow between two infinite parallel planes that move rel ative to each other at constant velocities or are at rest.…”

Section: Here Andmentioning

confidence: 99%

“…In [19] the values of were com puted up to three decimals for n = 1(1)3, R = 100, 45, , , . The method of regularized traces for computing approximate eigenvalues of differential operators was further developed in [25]. Specifically, let Т be a discrete lower semibounded Hermitian operator and Р be a bounded operator both defined in a separable Hilbert space Н.…”

Section: Here Andmentioning

confidence: 99%

“…A new method for computing to the practically required accuracy was proposed in [25]. The method is based on the Bubnov-Galerkin scheme as applied to the eigenvalue problem , (2.41) which can be written as .…”

Section: Here Andmentioning

confidence: 99%

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The theory of regularized traces of operators as applied to approximate computation of eigenvalues and eigenfunctions of fluid dynamics problems

Kerimov

2012

Comput. Math. and Math. Phys.

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Some results concerning the computation of eigenvalues and eigenfunctions of fluid dynamics problems by applying methods of regularized traces of differential operators are presented. The presentation is focused primarily on the non self adjoint fourth order Orr-Sommerfeld opera tor, which arises in the hydrodynamic stability theory of viscous flows. : approximate methods for problems concerning hydrodynamic stability of viscous flows, Orr-Sommerfeld differential operator, computation of eigenvalues and eigenfunctions, methods of regularized traces of operators. *( 1,0) y ∈ − COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS Vol. 52 No. 5 2012 KERIMOV ject. However, this paper overviews only results obtained by methods of regularized operator traces, which are a further development of Dorodnicyn's well known method for the approximate computation of eigenvalues and eigenfunctions of Sturm-Liouville operators (see [3]).

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confidence: 99%

Section: Here Andmentioning

confidence: 99%

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The theory of regularized traces of operators as applied to approximate computation of eigenvalues and eigenfunctions of fluid dynamics problems

Kerimov

2012

Comput. Math. and Math. Phys.

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“…Ключевые слова: асимптотические формулы; собственные значения и собственные функции; дискретные и самосопряженные операторы; обратные спектральные задачи; метод Галеркина. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] 6) 52cos( 4) 75cos( 2) 9cos( 8))…”

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Algorithms for the Computation of the Eigenvalues of Discrete Semi-Bounded Operators Defined on Quantum Graphs

Kadchenko,

Stavtceva,

Ryazanova

et al. 2023

MMPh

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Spectral problems for differential operators defined on quantum graphs are of great scientific interest related to problems in quantum mechanics, computer network modeling, image processing, ranking algorithms, modeling of electrical, and mechanical and acoustic processes, in networks of a diverse nature, in designing nano systems with prescribed properties and in other areas. Theoretical solutions of direct and inverse spectral problems on quantum graphs have been developed, but computational algorithms based on these methods are computationally inefficient. We have not seen any published works that consider examples of numerical solutions of spectral problems on finite connected graphs with a large number of vertices and edges. Therefore, the development of new computationally effective algorithms for numerical solution of spectral problems given on finite connected graphs is urgent. This paper develops a technique for finding the eigenvalues of boundary value problems on finite connected graphs with a required number of vertices and edges. To use this technique, it is necessary to know the eigenvalues and vectors of the eigenfunctions of corresponding unperturbed vector operators which are usually self-adjoint. Finding them manually, if the graph has a large number of vertices and edges, is difficult. This led to writing a package of programs in the mathematical environment Maple to find transcendental equations in the symbolic mode to calculate eigenvalues and find the eigenfunctions of unperturbed boundary value problems. Examples of calculating eigenvalues for a quantum graph which models an anthracene aromatic compound molecule are presented.

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An approximate solution of inverse spectral problem for perturbed self-adjoint operator

Zakirova

2016

2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)

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Computing the sums of Rayleigh-Schrödinger series of perturbed self-adjoint operators

Cited by 6 publications

References 2 publications

The theory of regularized traces of operators as applied to approximate computation of eigenvalues and eigenfunctions of fluid dynamics problems

The theory of regularized traces of operators as applied to approximate computation of eigenvalues and eigenfunctions of fluid dynamics problems

Algorithms for the Computation of the Eigenvalues of Discrete Semi-Bounded Operators Defined on Quantum Graphs

An approximate solution of inverse spectral problem for perturbed self-adjoint operator

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