The authors develop an algorithm for the numerical evaluation of the finite Hilbert transform, with respect to non-standard weight functions, by a product quadrature rule. In particular, this algorithm allows us to deal with the weight functions with algebraic and/or logarithmic singularities in the interval [−1, 1], by using the Chebyshev points as quadrature nodes. The practical application of the rule is shown to be straightforward and to yield satisfactory numerical results. Convergence theorems are also given, when the nodes are the zeros of certain classical Jacobi polynomials and the weight is defined as a generalized Ditzian-Totik weight.
The numerical evaluation of cauchy principal value integrals with non-standard weight functions / CRISCUOLO G; SCUDERI L.. - In: BIT. - ISSN 0006-3835. - 38:2(1998), pp. 256-274. [10.1007/BF02512366]
|Titolo:||The numerical evaluation of cauchy principal value integrals with non-standard weight functions|
|Data di pubblicazione:||1998|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/BF02512366|
|Appare nelle tipologie:||1.1 Articolo in rivista|