Error estimates for a Gaussian rule involving Bessel functions

TL;DR

This paper develops error estimates for Gaussian quadrature rules with weights involving Bessel functions, using averaged rules and a priori error approximations, validated by numerical examples.

Contribution

It introduces new error estimation techniques for Gaussian rules with Bessel function weights, enhancing accuracy analysis for such integrals.

Findings

Numerical examples confirm the effectiveness of the proposed error estimates.

A priori error approximations provide reliable bounds for Gaussian rules with Bessel weights.

Averaged Gaussian rules improve the estimation of quadrature errors.

Abstract

This paper deals with the estimation of the quadrature error of a Gaussian formula for weight functions involving fractional powers, exponentials and Bessel functions of the first kind. For this purpose, in this work the averaged and generalized averaged Gaussian rules are employed, together with a tentative a priori approximation of the error. The numerical examples confirm the reliability of these approaches.