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Investigation of Some Hypersingular Integral Equations on the Sphere

Investigation of Some Hypersingular Integral Equations on the Sphere Di erential Equations, Vol. 37, No. 10, 2001, pp. 1468{1479. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 10, 2001, pp. 1395{1405. Original Russian Text Copyright c 2001 by Zakharov, I. Lifanov, P. Lifanov. NUMERICAL METHODS Investigation of Some Hypersingular Integral Equations on the Sphere E. V. Zakharov, I. K. Lifanov, and P. I. Lifanov Air Force Engineering Academy, Moscow, Russia Received March 15, 2001 The present paper deals with hypersingular integral equations on the sphere to which the Neu- mann problem for the Laplace and Helmholtz equations can be reduced. We obtain some new spectral relations for spherical functions. For quadrature formulas of the type of discrete closed vortex laments for the corresponding hypersingular integrals, we prove the uniform convergence at all computation points lying outside arbitrary given neighborhoods of the poles. Numerical experiments show that these quadrature formulas converge in the integral sense on the entire sphere, the numerical solution of a hypersingular integral equation on the sphere by the method of discrete closed vortex laments uniformly converges to the exact solution at all com- putation points, and shifts of computation points in uence the accuracy of both the quadrature formulas and the solution of the integral http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Investigation of Some Hypersingular Integral Equations on the Sphere

Zakharov, E.; Lifanov, I.; Lifanov, P.
Differential Equations , Volume 37 (10) – Oct 9, 2004
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1013380501396
Publisher site
See Article on Publisher Site

Abstract

Di erential Equations, Vol. 37, No. 10, 2001, pp. 1468{1479. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 10, 2001, pp. 1395{1405. Original Russian Text Copyright c 2001 by Zakharov, I. Lifanov, P. Lifanov. NUMERICAL METHODS Investigation of Some Hypersingular Integral Equations on the Sphere E. V. Zakharov, I. K. Lifanov, and P. I. Lifanov Air Force Engineering Academy, Moscow, Russia Received March 15, 2001 The present paper deals with hypersingular integral equations on the sphere to which the Neu- mann problem for the Laplace and Helmholtz equations can be reduced. We obtain some new spectral relations for spherical functions. For quadrature formulas of the type of discrete closed vortex laments for the corresponding hypersingular integrals, we prove the uniform convergence at all computation points lying outside arbitrary given neighborhoods of the poles. Numerical experiments show that these quadrature formulas converge in the integral sense on the entire sphere, the numerical solution of a hypersingular integral equation on the sphere by the method of discrete closed vortex laments uniformly converges to the exact solution at all com- putation points, and shifts of computation points in uence the accuracy of both the quadrature formulas and the solution of the integral

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Differential Equations – Springer Journals

Published: Oct 9, 2004

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