Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776724 | Applied Numerical Mathematics | 2017 | 22 Pages |
Abstract
In this paper we propose a global method to approximate the derivatives of the weighted Hilbert transform of a given function fHp(fwα,t)=dpdtpâ¨0+âf(x)xâtwα(x)dx=p!â¨0+âf(x)(xât)p+1wα(x)dx, where pâ{1,2,â¦}, t>0, and wα(x)=eâxxα is a Laguerre weight. The right-hand integral is defined as the finite part in the Hadamard sense. The proposed numerical approach is convenient when the approximation of the function Hp(fwα,t) is required. Moreover, if there is the need, all the computations can be performed without differentiating the density function f. Numerical stability and convergence are proved in suitable weighted uniform spaces and numerical tests which confirm the theoretical estimates are presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Maria Carmela De Bonis, Donatella Occorsio,