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On the Eigenvalue Problem for the Discrete Analogue of the Laplace Operator in Spherical Coordinates.

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Title: On the Eigenvalue Problem for the Discrete Analogue of the Laplace Operator in Spherical Coordinates.
Authors: Stepanova, I. E.1 (AUTHOR) tet@ifz.ru, Shchepetilov, A. V.2 (AUTHOR), Kolotov, I. I.2 (AUTHOR)
Source: Computational Mathematics & Mathematical Physics. Jan2026, Vol. 66 Issue 1, p65-74. 10p.
Subjects: Laplacian operator, Spherical coordinates, Boundary value problems, Iterative methods (Mathematics), Eigenfunctions, Finite difference method, Eigenvalues, Green's functions
Abstract: The eigenvalue problem for the finite-differenced analogues of the Laplace operator in spherical coordinates is considered. Finding eigenvalues and eigenfunctions for the finite-differenced boundary settings is a useful tool when evaluating the conditions for the implementation of the so-called matrix sweep method. This method makes it possible to determine potentials in two cases: (a) when the discrete fundamental solution is known, and (b) if an additional a priori information on the boundary values of potentials is given. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mathematics & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: <searchLink fieldCode="JN" term="%22Computational+Mathematics+%26+Mathematical+Physics%22">Computational Mathematics & Mathematical Physics</searchLink>. Jan2026, Vol. 66 Issue 1, p65-74. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Laplacian+operator%22">Laplacian operator</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+coordinates%22">Spherical coordinates</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenfunctions%22">Eigenfunctions</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Green's+functions%22">Green's functions</searchLink>
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  Data: The eigenvalue problem for the finite-differenced analogues of the Laplace operator in spherical coordinates is considered. Finding eigenvalues and eigenfunctions for the finite-differenced boundary settings is a useful tool when evaluating the conditions for the implementation of the so-called matrix sweep method. This method makes it possible to determine potentials in two cases: (a) when the discrete fundamental solution is known, and (b) if an additional a priori information on the boundary values of potentials is given. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computational Mathematics & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1134/S0965542525701763
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      – Code: eng
        Text: English
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      – SubjectFull: Laplacian operator
        Type: general
      – SubjectFull: Spherical coordinates
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      – SubjectFull: Boundary value problems
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      – SubjectFull: Iterative methods (Mathematics)
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      – SubjectFull: Eigenfunctions
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      – SubjectFull: Finite difference method
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      – SubjectFull: Eigenvalues
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              Text: Jan2026
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