Numerical computation of hypersingular integrals on the real semiaxis

The procedure we employ here is based on a simple tool like the “truncated” Gaussian rule (see [5]), conveniently modified to remove numerical cancellation. We will consider functions G having different decays at infinity. The method is shown to be numerically stable and convergent and some error estimates in suitable Zygmund-type spaces are proved. Finally, some numerical tests which confirm the efficiency of the proposed procedures are presented.