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On Kufarev’s method of determining the parameters in the Schwarz- Christoffel integral. (English. Russian original) Zbl 0829.30005
Russ. Acad. Sci., Dokl., Math. 49, No. 3, 445-448 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 1, 14-16 (1994).
Let \(D_n\) be a polygonal domain, and let \(D_n (t)\) be obtained from \(D_n\) by introducing a rectilinear slit of length \(\Lambda_n (t)\). Let \(a_j(t)\), \(c(t)\) be the accessory parameters in the Schwarz- Christoffel map from the upper half plane \(H\) onto \(D_n (t)\). The authors show that these satisfy a nonlinear system of ordinary differential equations, with given initial values if the mapping from \(H\) to \(D_n\) is known. This system has a unique solution for small values of \(t\). In view of the work of Trefethen, this method will hardly be suited for effective polygonal mappings.
Reviewer: D.Gaier (Gießen)
30C30 Schwarz-Christoffel-type mappings