Geodesic
Method of boundary integral equations with hypersingular integrals in boundary-value problems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 114-125.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we formulate mathematical foundations of applications of boundary integral equations with strongly singular integrals understood in the sense of finite Hadamard value to numerical solution of certain boundary-value problems. We describe numerical schemes for solving boundary strongly singular equations based on quadrature formulas and the collocation method. Also, we make references to known results on the mathematical justification of the numerical methods described in the paper.
Keywords: hypersingular integral, boundary integral equation, boundary-value problem, numerical methods. 
@article{INTO_2019_160_a12,
     author = {A. V. Setukha},
     title = {Method of boundary integral equations with hypersingular integrals in boundary-value problems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {114--125},
     publisher = {mathdoc},
     volume = {160},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_160_a12/}
}
TY  - JOUR
AU  - A. V. Setukha
TI  - Method of boundary integral equations with hypersingular integrals in boundary-value problems
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 114
EP  - 125
VL  - 160
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_160_a12/
LA  - ru
ID  - INTO_2019_160_a12
ER  - 
%0 Journal Article
%A A. V. Setukha
%T Method of boundary integral equations with hypersingular integrals in boundary-value problems
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 114-125
%V 160
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_160_a12/
%G ru
%F INTO_2019_160_a12
A. V. Setukha. Method of boundary integral equations with hypersingular integrals in boundary-value problems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 114-125. http://geodesic.mathdoc.fr/item/INTO_2019_160_a12/

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

[2] Aparinov V. A., Dvorak A. V., “Metod diskretnykh vikhrei s zamknutymi vikhrevymi ramkami”, Tr. VVIA im. N. E. Zhukovskogo, 1986, no. 1313, 424–432

[3] Belotserkovskii S. M., Nisht M. I., Otryvnoe i bezotryvnoe obtekanie tonkikh krylev idealnoi zhidkostyu, Nauka, M., 1978

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

[5] Gutnikov V. A., Kiryakin V. Yu., Lifanov I. K. i dr., “O chislennom reshenii dvumernogo gipersingulyarnogo integralnogo uravneniya i o rasprostranenii zvuka v gorodskoi zastroike”, Zh. vychisl. mat. mat. fiz., 47:12 (2007), 2088–2100 | MR

[6] Davydov A. G., Zakharov E. V., Pimenov Yu. V., “Metod chislennogo resheniya zadach difraktsii elektromagnitnykh voln na nezamknutykh poverkhnostyakh proizvolnoi formy”, Dokl. RAN, 276:1 (1984), 96–100 | MR

[7] Daeva S. G., Setukha A. V., “O chislennom reshenii kraevoi zadachi neimana dlya uravneniya Gelmgoltsa metodom gipersingulyarnykh integralnykh uravnenii”, Vychisl. metody program. Novye vychisl. tekhnol., 16 (2015), 421–435

[8] Zakharov E. V., Ryzhakov G. V., Setukha A. V., “Chislennoe reshenie trekhmernykh zadach difraktsii elektromagnitnykh voln na sisteme idealnoprovodyaschikh poverkhnostei metodom gipersingulyarnykh integralnykh uravnenii”, Differ. uravn., 50:9 (2014), 1253–1263 | DOI | Zbl

[9] Zakharov E. V., Setukha A. V., Bezobrazova E. N., “Metod gipersingulyarnykh integralnykh uravnenii v trekhmernoi zadache difraktsii elektromagnitnykh voln na kusochno-odnorodnom dielektricheskom tele”, Differ. uravn., 51:9 (2015), 1206–1219 | DOI | Zbl

[10] Ilinskii A. S., Smirnov Yu. G., Difraktsiya elektromagnitnykh voln na provodyaschikh tonkikh ekranakh. Psevdodifferentsialnye operatory v zadachakh difraktsii, IPRZhR, M., 1996

[11] Kolton D., Kress R., Metody integralnykh uravnenii v teorii rasseyaniya, Mir, M., 1987

[12] Lebedeva S. G., Setukha A. V., “O chislennom reshenii polnogo dvumernogo gipersingulyarnogo uravneniya metodom diskretnykh osobennostei”, Differ. uravn., 49:2 (2013), 223–233 | Zbl

[13] Lifanov I. K., Metod singulyarnykh integralnykh uravnenii i chislennyi eksperiment, Yanus, M., 1995

[14] Piven V. F., Matematicheskie modeli filtratsii zhidkosti, OGU, Orel, 2015

[15] Ryzhakov G. V., Setukha A. V., “O skhodimosti chislennogo metoda resheniya nekotorogo gipersingulyarnogo integralnogo uravneniya na zamknutoi poverkhnosti”, Differ. uravn., 46:9 (2010), 1343–1353 | MR | Zbl

[16] Setukha A. V., “Kraevaya zadacha Neimana s granichnym usloviem na razomknutoi ploskoi poverkhnosti”, Differ. uravn., 37:10 (2001), 1320–1338 | MR

[17] Setukha A. V., “O postroenii fundamentalnykh reshenii kraevoi zadachi Neimana v oblasti vne razomknutoi ploskoi poverkhnosti”, Differ. uravn., 38:4 (2002), 505–515 | MR | Zbl

[18] Setukha A. V., “Trekhmernaya kraevaya zadacha Neimana s obobschennymi granichnymi usloviyami i uravnenie Prandtlya”, Differ. uravn., 39:9 (2003), 1188–1200 | MR | Zbl

[19] Smirnov Yu. G., Matematicheskie metody issledovaniya zadach elektrodinamiki, Inf.-izd. tsentr PenzGU, Penza, 2009

[20] John L. V., Kubilay S., Integral Equation Methods for Electromagnetics, SciTech Publ., 2012

[21] McLean W., Strongly Elliptic Systems and Boundary Integral Equations, Cambridge Univ. Press, 2000 | MR | Zbl

[22] Rao S. M., Wilton D. R., Glisson A. W., “Electromagnetic scattering by surfaces of arbitrary shape”, IEEE Trans. Antennas Propag., 30:3 (1982), 409–418 | DOI | MR

[23] Setukha A. V., Bezobrazova E. N., “The method of hypersingular integral equations in the problem of electromagnetic wave diffraction by a dielectric body with a partial perfectly conducting coating”, Russ. J. Numer. Anal. Math. Model., 32:6 (2017), 371–380 | DOI | MR | Zbl