A Chebyshev polynomial based quadrature for hypersingular integrals - Obaiys, Suzan J.; Eshkuvatov, Zainidin K.; Nik Long, Nik Mohd Asri (American Institute of Physics, 2011)
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.