Numerical quadrature for Bessel transformations

Authors:
Shuhuang Xiang;Weihua Gui;Pinghua Mo
Affiliations:
Department of Applied Mathematics and Software, Central South University, Changsha, Hunan 410083, China;College of Information Science and Engineering, Central South University, Changsha, Hunan 410083, China;Department of Applied Mathematics and Software, Central South University, Changsha, Hunan 410083, China
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 8
Cited 1

A method for computing Bessel function integrals

Journal of Computational Physics
Fast integration of rapidly oscillatory functions

Journal of Computational and Applied Mathematics
A high order, progressive method for the evaluation of irregular oscillatory integrals

Applied Numerical Mathematics
Analysis of a collocation method for integrating rapidly oscillatory functions

Journal of Computational and Applied Mathematics
Some theoretical aspects of generalised quadrature methods

Journal of Complexity
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation

SIAM Journal on Numerical Analysis
Efficient Filon-type methods for $$\int_a^bf(x)\,{\rm e}^{{\rm i}\omega g(x)}\,{\rm d}x$$

Numerische Mathematik

Numerical Quadrature for Bessel Transformations with High Oscillations

Numerical Analysis and Its Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we explore higher order numerical quadratures for the integration of systems containing Bessel functions. Two families of methods are presented. One is based on a truncation of the asymptotic series and the other is extending an approach in the work of Levin. The decay of the error drastically improves as frequency grows. The effectiveness and accuracy of the quadrature is tested for large arguments of Bessel functions.