This paper proposes an automatic quadrature scheme (AQS) for evaluating the hypersingular integrals with weight function w(t)=1 on the interval [0,1]. The density function f (x) is approximated by the shifted Chebyshev polynomials P∗N(t) of the first kind of degree N. AQS for Cauchy principle value integrals on the interval [0,1] is also considered. Numerical examples are demonstrated in order to show that our developed approach can provide effective and reliable results.
Obaiys, Suzan J. and Eshkuvatov, Zainidin K. and Nik Long, Nik Mohd Asri (2012) A Chebyshev polynomial based quadrature for hypersingular integrals. In: 5th International Conference on Research and Education in Mathematics, 1-3 Nov. 2011, Bandung, Indonesia. pp. 139-141.
A Chebyshev polynomial based quadrature for hypersingular integrals.
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