Numerical method for hypersingular integrals of highly oscillatory functions on the positive semiaxis

Abstract

This paper deals with a quadrature rule for the numerical evaluation of hypersingular integrals of highly oscillatory functions on the positive semiaxis. The rule is of product type and consists in approximating the density function f by a truncated interpolation process based on the zeros of generalized Laguerre polynomials and an additional point. We prove the stability and the convergence of the rule, giving error estimates for functions belonging to weighted Sobolev spaces equipped with uniform norm. We also show how the proposed rule can be used for the numerical solution of hypersingular integral equations. Numerical tests which confirm the theoretical estimates and comparisons with other existing quadrature rules are presented.

De Bonis M. C., Sagaria V. (2022) "Numerical method for hypersingular integrals of highly oscillatory functions on the positive semiaxis " Dolomites Research Notes on Approximation, 15(3), 49-64. DOI: 10.14658/PUPJ-DRNA-2022-3-6  
Year of Publication
2022
Journal
Dolomites Research Notes on Approximation
Volume
15
Issue Number
3
Start Page
49
Last Page
64
Date Published
10/2022
ISSN Number
2035-6803
Serial Article Number
6
DOI
10.14658/PUPJ-DRNA-2022-3-6
Issue
Section
SpecialIssue3