Geodesic
On the determination of constants in the Schwarz–Christoffel integral by P. P. Kufarev's method
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2016), pp. 21-27

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

Schwarz–Christoffel's integral maps simple-connected polygonal domains onto the upper half-plain and is successfully used in various applications related to problems of hydrodynamics, electrodynamics, and elasticity theory. The main difficulty in the practical use of this integral is in the determination of parameters entering into it. This paper investigates P. P. Kufarev's method (1947) for the numerical determination of parameters involved in the Schwarz–Christoffel transformation. In this method, the difficult problem of determining parameters is reduced to an easier one, namely, to numerical integration of a system of ordinary differential equations. These equations describe the motion of preimages of polygon vertices. The paper presents an analysis of Kufarev's equations and describes properties of this transformation. The problem of initial conditions and a way to solve it are also considered. Determining constants in the Schwarz–Christoffel integral by Kufarev's method has a reliable theoretical basis, and the properties of this method are corroborated by calculations.
Keywords: conformal mapping of rectilinear polygons, direct images and counter images of vertices, streamlines. 
S. Jambaa; T. V. Kasatkina; A. M. Bubenchikov. On the determination of constants in the Schwarz–Christoffel integral by P. P. Kufarev's method. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2016), pp. 21-27. http://geodesic.mathdoc.fr/item/VTGU_2016_5_a1/
@article{VTGU_2016_5_a1,
     author = {S. Jambaa and T. V. Kasatkina and A. M. Bubenchikov},
     title = {On the determination of constants in the {Schwarz{\textendash}Christoffel} integral by {P.} {P.~Kufarev's} method},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {21--27},
     year = {2016},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2016_5_a1/}
}
TY  - JOUR
AU  - S. Jambaa
AU  - T. V. Kasatkina
AU  - A. M. Bubenchikov
TI  - On the determination of constants in the Schwarz–Christoffel integral by P. P. Kufarev's method
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2016
SP  - 21
EP  - 27
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VTGU_2016_5_a1/
LA  - ru
ID  - VTGU_2016_5_a1
ER  - 
%0 Journal Article
%A S. Jambaa
%A T. V. Kasatkina
%A A. M. Bubenchikov
%T On the determination of constants in the Schwarz–Christoffel integral by P. P. Kufarev's method
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2016
%P 21-27
%N 5
%U http://geodesic.mathdoc.fr/item/VTGU_2016_5_a1/
%G ru
%F VTGU_2016_5_a1

[1] Koppenfels W., Stallmann F., Praxis der konformen abbildung, Springer-Verlag, Berlin–Gottingen–Heidelberg, 1959, 375 pp. | MR | Zbl

[2] Fil'chakov P. F., Numerical and graphical methods of applied mathematics, Naukova Dumka, Kiev, 1972

[3] Kantorovich L. V., Krylov V. I., Approximate methods of higher analysis, Gos. izd-vo tekhniko-teoreticheskoy literatury, L.–M., 1949

[4] Kufarev P. P., “A method for determining the parameters of the Schwarz–Christoffel integral”, Dokl. Akad. Nauk SSSR, 57 (1947), 535–537 | MR | Zbl

[5] Aleksandrov I. A., Parametric continuations in the theory of one-sheeted functions, Nauka, M., 1976 | MR