On spline Galerkin methods for singular integral equations with piecewise continuous coefficients
A system of singular integral equations of Cauchy type with piecewise continuous coefficients is considered. The convergence of the Galerkin method with polynomial splines for such systems is investigated. The method is proved to be convergent only for strongly elliptic integral operators. Error estimates are provided for various partitions. It is the reviewer's opinion that the Galerkin method is far from being the most suitable one for singular integral equations [See \textit{T. S. Sankar}, \textit{S. V. Hoa} and the reviewer in Int. J. Numer. Methods Eng. 18, 503- 519 (1982; Zbl 0495.73073) and in Comput. Methods Appl. Mech. Eng. 29, 19-33 (1981; Zbl 0468.65067)].
scientific article; zbMATH DE number 4005565
scientific article