pylevin: Efficient numerical integration of integrals containing up to three Bessel functions

TL;DR

pylevin is a Python package that efficiently computes highly oscillatory integrals with up to three Bessel functions, outperforming standard methods in speed and stability for complex integrals.

Contribution

The paper introduces pylevin, a novel Python tool that extends efficient numerical integration to integrals with multiple Bessel functions, surpassing existing methods in speed and stability.

Findings

pylevin achieves comparable speed to specialized packages for single Bessel integrals.

It is up to 10,000 times faster than standard adaptive quadrature for multiple Bessel functions.

pylevin exhibits improved stability for large argument integrals.

Abstract

Integrals involving highly oscillatory Bessel functions are notoriously challenging to compute using conventional integration techniques. While several methods are available, they predominantly cater to integrals with at most a single Bessel function, resulting in specialised yet highly optimised solutions. Here we present pylevin, a Python package to efficiently compute integrals containing up to three Bessel functions of arbitrary order and arguments. The implementation makes use of Levin's method and allows for accurate and fast integration of these highly oscillatory integrals. In benchmarking pylevin against existing software for single Bessel function integrals, we find its speed comparable, usually within a factor of two, to specialised packages such as FFTLog. Furthermore, when dealing with integrals containing two or three Bessel functions, pylevin delivers performance up to four orders of magnitude faster than standard adaptive quadrature methods, while also exhibiting better stability for large Bessel function arguments. pylevin is available from source via github or directly from PyPi.