Modified Schwarz alternating method to the solution of the Riemann--Hilbert problem on doubly connected domains

Abstract

The article is devoted to the solution of a Riemann--Hilbert boundary value problem on a doubly connected unbounded domain by a modification of the Schwarz alternating method. The obtained solution is given by the series. Each element of this series represents the solution of the corresponding Riemann--Hilbert problem on a simply connected circular domain. The operator corresponding to the formula of the solution is also proposed. Convergence of the method is shown.