On a~method of calculation of hypersingular integrals
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 3-17.

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We propose an analytic method for calculation of one-dimensional and two-dimensional hypersingular integrals. Based on this method, we construct approximate method for calculation of one-dimensional and two-dimensional hypersingular integrals having singularities on rather complicated manifolds. We give estimates of errors of suggested algorithms.
Keywords: hypersingular integrals, cubature formulas.
Mots-clés : quadrature formulas
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I. V. Boikov; M. A. Semov. On a~method of calculation of hypersingular integrals. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 3-17. http://geodesic.mathdoc.fr/item/IVM_2016_3_a0/

[1] Adamar Zh., Zadacha Koshi dlya lineinykh uravnenii s chastnymi proizvodnymi giperbolicheskogo tipa, Nauka, M., 1978 | MR

[2] Samko S. G., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987 | MR

[3] Samko S. G., Hypersingular integrals and their applications, Taylor and Frencis, London–New York, 2002 | MR | Zbl

[4] Benerdzhi P., Metod granichnykh elementov v prikladnykh zadachakh, Mir, M., 1984

[5] Boykov I. V., Boykova A. I., Ventsel E. S., “Fundamental solutions for thick sandwich plates”, Engineering Analysis with Boundary Elements, 28:12 (2004), 1437–1444 | DOI | Zbl

[6] Boykov I. V., “Numerical methods of computation of singular and hypersingular integrals”, Intern. J. Math. and Math. Sci., 28:3 (2001), 127–179 | DOI | MR

[7] Boykov I. V., Boykova A. I., Ventsel E. S., “An approximation methods for evaluating hypersingular integrals”, Engineering Analysis with Boundary Elements, 30:9 (2006), 799–807 | DOI | Zbl

[8] Boykov I. V., Ventsel E. S., Boykova A. I., “Accuracy optimal methods for evaluating hypersingular integrals”, Appl. Numer. Math., 59:6 (2009), 1366–1385 | DOI | MR | Zbl

[9] Boikov I. V., Priblizhennye metody vychisleniya singulyarnykh i gipersingulyarnykh integralov. Ch. 2. Gipersingulyarnye integraly, Izd-vo Penzensk. gos. un-ta, Penza, 2009 | MR | Zbl

[10] Vainikko G. M., Lifanov I. K., Poltavskii L. N., Chislennye metody v gipersingulyarnykh integralnykh uravneniyakh i ikh prilozheniya, Yanus-K, M., 2001

[11] Chikin L. A., “Osobye sluchai kraevoi zadachi Rimana i singulyarnykh integralnykh uravnenii”, Uchen. zap. Kazansk. gos. un-ta, 113, no. 10, 1953, 57–105

[12] Boikov I. V., Optimalnye metody priblizheniya funktsii i vychisleniya integralov, Izd-vo Penzensk. gos. un-ta, Penza, 2007 | MR

[13] Natanson I. P., Konstruktivnaya teoriya funktsii, Gostekhizdat, M.–L., 1949

[14] Linkov A. M., Kompleksnyi metod granichnykh integralnykh uravnenii teorii uprugosti, Nauka, M., 1999