Geodesic
Computing experiments in the problem on eigenvalues for the operator of Laplace in the polygonal domain
Matematičeskoe modelirovanie, Tome 23 (2011) no. 7, pp. 88-96.

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

The technique of a numerical evaluation of eigenvalues of an operator of Laplace in a polygon is described. As an example it is considered L-figurative area. The circle conformal mapping on this area by means of an integral of Christoffel–Schwarz is under construction. In a circle the problem dares on earlier developed by the author (together with K. I. Babenko) a technique without saturation. The problem consists in, whether this technique to piecewise smooth boundaries (the conformal mapping has on singularity boundary) is applicable. The done evaluations show that it is possible to calculate about 5 eigenvalues (for a problem of Neumann about 100 eigenvalues) an operator of Laplace in this area with two-five signs after a comma.
Keywords: eigenvalues of an operator of Laplace, an integral of Christoffel-Schwarz, numerical algorithm without saturation. 
@article{MM_2011_23_7_a6,
     author = {S. D. Algazin},
     title = {Computing experiments in the problem on eigenvalues for the operator of {Laplace} in the polygonal domain},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {88--96},
     publisher = {mathdoc},
     volume = {23},
     number = {7},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_7_a6/}
}
TY  - JOUR
AU  - S. D. Algazin
TI  - Computing experiments in the problem on eigenvalues for the operator of Laplace in the polygonal domain
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 88
EP  - 96
VL  - 23
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_7_a6/
LA  - ru
ID  - MM_2011_23_7_a6
ER  - 
%0 Journal Article
%A S. D. Algazin
%T Computing experiments in the problem on eigenvalues for the operator of Laplace in the polygonal domain
%J Matematičeskoe modelirovanie
%D 2011
%P 88-96
%V 23
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_7_a6/
%G ru
%F MM_2011_23_7_a6
S. D. Algazin. Computing experiments in the problem on eigenvalues for the operator of Laplace in the polygonal domain. Matematičeskoe modelirovanie, Tome 23 (2011) no. 7, pp. 88-96. http://geodesic.mathdoc.fr/item/MM_2011_23_7_a6/

[1] T. A. Driscoll, L. N. Trefethen, Schwarz-Christoffel Mapping, Cambridge University Press, Cambridge, UK, 2002 | MR | Zbl

[2] S. D. Algazin, Chislennye algoritmy klassicheskoi matematicheskoi fiziki, Dialog-MIFI, M., 2010, 240 pp.

[3] S. D. Algazin, Chislennye algoritmy klassicheskoi matematicheskoi fiziki. XI. O vychislenii sobstvennykh znachenii uravneniya perenosa, Prepr. IPMekh, No 801, M., 2006, 16 pp.

[4] S. D. Algazin, “O vychislenii sobstvennykh znachenii uravneniya perenosa”, PMTF, 45:4 (2004), 107–113 | MR | Zbl

[5] S. D. Algazin, Chislennye algoritmy klassicheskoi matfiziki. XXX. Vychislenie sobstvennykh znachenii operatora Laplasa v mnogougolnoi oblasti, Prepr. IPMekh, No 970, M., 2011, 16 pp.

[6] K. I. Babenko, Osnovy chislennogo analiza, 2-e izd., ispr. i dop., ed. A. D. Bryuno, Nauka, M., 1986, 744 pp. | MR