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Application of Quadrature Formulas for a Single-Layer Potential for an Exterior Neumann Problem.

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Title: Application of Quadrature Formulas for a Single-Layer Potential for an Exterior Neumann Problem.
Authors: Krutitskii, P. A.1 (AUTHOR) biem@mail.ru, Reznichenko, I. O.1 (AUTHOR) io.reznichenko@physics.msu.ru
Source: Computational Mathematics & Mathematical Physics. Jul2025, Vol. 65 Issue 7, p1520-1534. 15p.
Subjects: Neumann problem, Laplace's equation, Numerical integration, Gaussian quadrature formulas, Error analysis in mathematics, Ellipsoids, Potential functions, Simulation methods & models
Abstract: For an exterior Neumann problem, a numerical method is proposed based on new quadrature formulas for a single-layer potential, which are based on the analytical evaluation of integrals. The method is tested on the Neumann problem for the Laplace equation outside an ellipsoid, for which explicit solutions are found. It is shown that the numerical solution of the problem produced by the proposed method uniformly approximates the exact solution and ensures a lower error and faster convergence than the numerical solution obtained using standard quadrature formulas based on numerical integration. The properties of numerical solutions depending on the parameters of the ellipsoid are discussed. [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.)
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  Data: Application of Quadrature Formulas for a Single-Layer Potential for an Exterior Neumann Problem.
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  Data: <searchLink fieldCode="JN" term="%22Computational+Mathematics+%26+Mathematical+Physics%22">Computational Mathematics & Mathematical Physics</searchLink>. Jul2025, Vol. 65 Issue 7, p1520-1534. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Neumann+problem%22">Neumann problem</searchLink><br /><searchLink fieldCode="DE" term="%22Laplace's+equation%22">Laplace's equation</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+integration%22">Numerical integration</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+quadrature+formulas%22">Gaussian quadrature formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Ellipsoids%22">Ellipsoids</searchLink><br /><searchLink fieldCode="DE" term="%22Potential+functions%22">Potential functions</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink>
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  Data: For an exterior Neumann problem, a numerical method is proposed based on new quadrature formulas for a single-layer potential, which are based on the analytical evaluation of integrals. The method is tested on the Neumann problem for the Laplace equation outside an ellipsoid, for which explicit solutions are found. It is shown that the numerical solution of the problem produced by the proposed method uniformly approximates the exact solution and ensures a lower error and faster convergence than the numerical solution obtained using standard quadrature formulas based on numerical integration. The properties of numerical solutions depending on the parameters of the ellipsoid are discussed. [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/S096554252570068X
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        Text: English
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        Type: general
      – SubjectFull: Laplace's equation
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      – SubjectFull: Numerical integration
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      – SubjectFull: Gaussian quadrature formulas
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      – SubjectFull: Error analysis in mathematics
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      – SubjectFull: Ellipsoids
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      – SubjectFull: Potential functions
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      – SubjectFull: Simulation methods & models
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              Text: Jul2025
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              Y: 2025
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