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Numerical evaluation of hypersingular integrals. (English) Zbl 0818.65016
The paper is motivated by the occurrence of singular and hypersingular integrals in applied mathematics, for example Cauchy principal value and Hadamard finite-part integrals in boundary integral equations. Attention is concentrated on the less familiar two-dimensional Cauchy principal value integrals and one- and two-dimensional integrals with stronger singularities requiring interpretation as finite-part integrals.
Basic definitions and properties are discussed. Methods for the numerical evaluation of these integrals are critically reviewed and a number of new results on convergence, expressions for weights, asymptotic error estimates and conditioning of rules (stability factors) are obtained. Numerical examples are included.

MSC:
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
41A63 Multidimensional problems
41A80 Remainders in approximation formulas
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