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Numerical methods on graded meshes for singular integral equations with conjugation. (English) Zbl 1066.65161
Summary: We consider simple methods for the numerical solution of Cauchy singular integral equations with conjugation based on quadratures. They use collocation at a set of nodes which is graded toward the endpoints, to accomodate for the presence of the singularity. Our numerical experience reveals that the theoretical stability findings are indeed of practical applicability, as the empirical condition number is seen very often to reach a plateau, whose asymptotic value is indeed very low.

65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type