Geodesic
Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1294-1303 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A singular integral equation with a Cauchy kernel and a logarithmic singularity on its righthand side is considered on a finite interval. An algorithm is proposed for the numerical solution of this equation. The contact elasticity problem of a Рџ-shaped rigid punch indented into a half-plane is solved in the case of a uniform hydrostatic pressure occurring under the punch, which leads to a logarithmic singularity at an endpoint of the integration interval. The numerical solution of this problem shows the efficiency of the proposed approach and suggests that the singularity has to be taken into account in solving the equation. 
@article{ZVMMF_2017_57_8_a5,
     author = {H. Amirjanyan and A. V. Sahakyan},
     title = {Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1294--1303},
     year = {2017},
     volume = {57},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a5/}
}
TY  - JOUR
AU  - H. Amirjanyan
AU  - A. V. Sahakyan
TI  - Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 1294
EP  - 1303
VL  - 57
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a5/
LA  - ru
ID  - ZVMMF_2017_57_8_a5
ER  - 
%0 Journal Article
%A H. Amirjanyan
%A A. V. Sahakyan
%T Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 1294-1303
%V 57
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a5/
%G ru
%F ZVMMF_2017_57_8_a5
H. Amirjanyan; A. V. Sahakyan. Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1294-1303. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a5/

[1] Sadowski M. L., “Zweidimensionale Probleme der Elastizitats-theorie”, ZAMM, 8:2 (1928)

[2] Shtaerman I. Ya., Kontaktnaya zadacha teorii uprugosti, Gostekhteorizdat, M.–L., 1997

[3] Galin L. A., Kontaktnye zadachi teorii uprugosti i vyazkouprugosti, Nauka, M., 1980

[4] Amirdzhanyan A. A., Saakyan A. V., “O vdavlivanii zhestkogo shtampa s vognutym osnovaniem v upruguyu poluploskost s uchetom vliyaniya napolnitelya v kaverne”, Izvestiya NAN RA. Mekhanika, 65:1 (2012), 7–16 http://mechanics.asj-oa.am/1994/1/03AmirjSah7-16.pdf

[5] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968

[6] Sahakyan A. V., “Method of discrete singularities for solution of singular integral and integro-differ-ential equations”, Proc. of A. Razmadze Mathematical Institute, 156 (2011), 101–111 http://www.mechins.sci.am/publ/avetik_sahakyan/RazmadzeProceedings.pdf | MR | Zbl