Gaussian rule for integrals involving Bessel functions

TL;DR

This paper develops a Gaussian quadrature rule tailored for integrals with weights involving fractional powers, exponentials, and Bessel functions, introducing a stable computational algorithm and demonstrating its practical application.

Contribution

It introduces a new stable algorithm for Gaussian quadrature with Bessel function weights, enhancing computational efficiency and accuracy.

Findings

Algorithm based on preconditioning improves stability.

Numerical experiments validate the method's effectiveness.

Application demonstrated in geophysical context.

Abstract

In this work we develop the Gaussian quadrature rule for weight functions involving fractional powers, exponentials and Bessel functions of the first kind. Besides the computation based on the use of the standard and the modified Chebyshev algorithm, here we present a very stable algorithm based on the preconditioning of the moment matrix. Numerical experiments are provided and a geophysical application is considered.