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Collocation and quadrature methods for solving singular integral equations with piecewise continuous coefficients. (English) Zbl 1124.65121
The author investigates computation schemes of collocation and mechanical quadrature methods for an approximate solving of complete singular integral equations with piecewise continuous coefficients, a weakly singular and regular kernel using the Arzela-Ascoli theorem and the Banach theorem in operator theory based on the theory of classical singular integral equations of analytic functions with one complex variable.
65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type
45F15 Systems of singular linear integral equations
45G05 Singular nonlinear integral equations