2023/02/08 by A. Posadskii, Posadskii, A., С. Р. Насыров +1
Mathematics · #30C30 (Primary) 30-08 (Secondary) #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2302.04350
openalex publication_date 2023/02/08 · openalex created_date 2023/02/13 · openalex updated_date 2026/07/28
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.