Numerical computation of hypersingular integrals on the real semiaxis

In this paper we propose some different strategies to approximate hypersingular integrals ∫=0+∞G(x)(x−t)p+1dx,where p is a positive integer, t > 0 and the integral is understood in the Hadamard finite part sense. Hadamard Finite Part integrals (shortly FP integrals), regarded as pth derivative of Cauchy principal value integrals, are of interest in the solution of hypersingular BIE, which model many different kind of Physical and Engineering problems (see [1] and the references therein, [2], [3, 4]).

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