Automatic quardrature sceheme for evaluating hypersingular intergrals. - Obaiys, Susan J.; Eshkuratov, Zainidin K.; Nik Long, Nik Mohd Asri (World Scientific Publishing Company, 2012)

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Hasegawa constructed the automatic quadrature scheme (AQS), of Cauchy principle value integrals for smooth functions. There is a close connection between Hadamard and Cauchy principle value integral. In this paper, we modify AQS for hypersingular integrals with second-order singularities, using hasegawa’s formula and based on therelations between Hadamard finite part integral and Cauchy principle value integral.Numerical experiments are also given, to validate the modified AQS.