Geodesic
Numerical solution of a problem about the parameters of a conformal mapping
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 3, pp. 32-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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A converging cyclic iteration method is applied for finding the parameters of a conformal mapping of the upper half-plane onto the domain bounded by a given polygon. The numerical realization of the method is presented with a proof of convergence and an estimate of the convergence speed. A few examples of computer calculations is given. 
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Y. V. Gubkina; I. B. Davydkin; V. N. Monakhov. Numerical solution of a problem about the parameters of a conformal mapping. Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 3, pp. 32-39. http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a4/

[1] Monakhov V. N., “Ob odnom variatsionnom metode resheniya zadach gidrodinamiki so svobodnymi granitsami”, Sib. mat. zhurn., 41:5 (2000), 1106–1121 | MR | Zbl

[2] Weinstein A., “Der Kontinuitätsbeweis des Abbildungssatzes für Polygone”, Math. Z., 19 (1924), 72–84 | DOI | MR

[3] Leray J., Weinstein A., “Sur un probleme de representation conforme pose par la theorie de Helmholtz”, Comp. Rend. Acad. Sci., 198 (1934), 430–433

[4] Lavrentev M. A., “O nekotorykh svoistvakh odnolistnykh funktsii s prilozheniyami k teorii strui”, Mat. sb., 4 (1938), 391–458

[5] Monakhov V. N., Kraevye zadachi so svobodnymi granitsami dlya ellipticheskikh sistem uravnenii, Nauka, Novosibirsk, 1977 | MR

[6] Gubkina E. V., Monakhov V. N., “Filtratsiya zhidkosti so svobodnymi granitsami v neogranichennykh oblastyakh”, Prikl. mekhanika i tekhn. fizika, 41:5 (2000), 188–197 | MR

[7] Polubarinova-Kochina P. Ya., Teoriya dvizheniya gruntovykh vod, Nauka, M., 1977 | MR

[8] Aravin V. N., Numerov S. N., Teoriya dvizheniya zhidkostei i gazov v nedeformiruemoi poristoi srede, Gostekhteorizdat, M., 1955

[9] Filchakov P. F., Teoriya filtratsii pod gidrotekhnicheskimi sooruzheniyami, Izd-vo AN USSR, Kiev, 1959

[10] Driscoll T., Trefethen L., Schwarz–Christoffel Mapping, Univ. Press, Cambridge, 2002 | MR | Zbl

[11] Filchakov P. F., Chislennye i graficheskie metody prikladnoi matematiki, Nauk. dumka, Kiev, 1970 | MR