A quadrature formula for the derivative of logarithmic potentials
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 68 (2020), pp. 5-22 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new method for constructing a quadrature formula for a curvilinear singular integral is given, and on the basis of this method, quadrature formulas for the derivative of the logarithmic potential of a simple layer and the normal derivative of the logarithmic potential of a double layer are constructed.
Mots-clés : quadrature formula
Keywords: curvilinear singular integral, derivative of the logarithmic potential of a simple layer, normal derivative of the logarithmic potential of a double layer.
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M. N. Bakhshaliyeva. A quadrature formula for the derivative of logarithmic potentials. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 68 (2020), pp. 5-22. http://geodesic.mathdoc.fr/item/VTGU_2020_68_a0/

[1] D. L. Colton, R. Kress, Integral Equation Methods in Scattering Theory, John Wiley Sons, 1983 | MR | Zbl

[2] E. H. Khalilov, “Some properties of the operators generated by a derivative of the acoustic double layer potential”, Siberian Mathematical Journal, 55:3 (2014), 564–573 | DOI | MR | Zbl

[3] E. H. Khalilov, “Cubic formula for the normal derivative of a double layer acoustic potential”, Transactions of NAS of Azerbaijan, series of physical-technical and mathematical sciences, 34:1 (2014), 73–82 http://imm.az/journals/AMEA_xeberleri/cild34_N1_2014/meqaleler/73-82.pdf | Zbl

[4] E. H. Khalilov, “On an approximate solution of a class of boundary integral equations of the first kind”, Differential Equations, 52:9 (2016), 1234–1240 | DOI | MR | Zbl

[5] E. H. Khalilov, “Justification of the collocation method for a class of surface integral equations”, Mathematical Notes, 107:4 (2020), 663–678 | DOI | MR | Zbl

[6] N. I. Muskhelishvili, Singular Integral Equations, Springer Netherlands, 1958 | MR

[7] V. S. Vladimirov, Equations of Mathematical Physics, Marcel Dekker, New York, 1971 | MR | MR | Zbl

[8] E. H. Khalilov, M. N. Bakhshaliyeva, “Quadrature formulas for simple and double layer logarithmic potentials”, Proceedings of IMM of NAS of Azerbaijan, 45:1 (2019), 155–162 http://proc.imm.az/volumes/45-1/45-01-12.pdf | MR | Zbl

[9] Yu. A. Kustov, B. I. Musaev, The cubature formula for a two-dimensional singular integral and its applications, Submitted to VINITI, No 4281-81, 1981

[10] M. N. Bakhshaliyeva, “On the properties of operator generated by the direct value of the derivative of simple layer logarithmic potential”, Caspian Journal of Applied Mathematics, Ecology and Economics, 7:1 (2019), 11–24 | MR

[11] E. H. Khalilov, M. N. Bakhshaliyeva, “On the derivative of the double-layer logarithmic potential”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics, 2019, no. 62, 38–54 | DOI