One-Parameter Families of Conformal Mappings of the Half-Plane onto Polygonal Domains with Several Slits

被引：3

作者：

Posadskii, A. ^{[1
,2
]}

Nasyrov, S. ^{[2
,3
]}

机构：

[1] Lebedev Phys Inst, Moscow 119991, Russia

[2] St Petersburg Univ, St Petersburg 199034, Russia

[3] Kazan Fed Univ, Kazan 420008, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 04期

关键词：

Schwarz-Christoffel integral; accessory parameters; Loewner equation; parametric method; Kufarev method; Cauchy problem; ODE system; CHRISTOFFEL; COMPUTATION;

D O I：

10.1134/S1995080223040224

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Among various methods of finding accessory parameters in the Schwarz-Christoffel integrals, Kufarev's method, based on the Loewner differential equation, plays an important role. It is used for describing one-parameter families of functions that conformally map a canonical domain onto a polygon with a slit the endpoint of which moves along a polygonal line starting from a boundary point. We present a modification of Kufarev's method for the case of several slits, the lengths of which have depend of each other in a certain way. We justify the method and find a system of ODEs describing the dynamics of accessory parameters. We also present the results of numerical calculations which confirm the efficiency of our method.

引用

页码：1448 / 1463

页数：16

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