A numerical method for singular integral equations with conjugation is studied. For the first time, such, kind of methods (the method of discrete vortices) was presented by S.M.Belotserkovskii in the middle of the 50-s when he was studying some problems of aerodynamics. Twenty years after I.K.Lifanov and Ya.E.Polonsky proved its stability for singular integral equations without conjugation and with a special choice of the coefficients. A.Rathsfeld, S.Proessdorf and S.Roch generalized these results on the case of variable coefficients and complicated curves. It was shown that the stability of the method depends on the invertibility of certain associate operators. In the present paper our aim is to establish conditions, which guarantee that indices of such operators are equal to zero.
展开▼
