On the problem of determining parameters in the Schwarz equation

Abstract

P. P. Kufarev’s method makes it possible to reduce the problem of determining the parameters in the Schwarz-Christoffel integral to the problem of successive solutions of systems of ordinary differential equations. B. G. Baibarin obtained a generalization of this method for the problem of determining parameters (preimages of vertices and accessory parameters) in the Schwarz differential equation, whose solution is a holomorphic univalent mapping from the upper half-plane onto a circular-arc polygon. This paper specifies the initial condition for the system of differential equations for the parameters of the Schwarz equation obtained by B. G. Baibarin. This method is used to solve the problem of determining the accessory parameters for some particular mappings.