Numerical computation of infinite Bessel transforms with high frequency

ABSTRACT

In this paper numerical evaluation of infinite Bessel transforms with high frequency is considered. We first derive an asymptotic formula by using the integration by parts. Next we use an interpolation formula to evaluate the infinite Bessel transforms by choosing the suitable basis and nodes. The corresponding error results are proved, and numerical examples are shown to illustrate the efficiency and accuracy of the presented formulae.

KEYWORDS:

• Numerical integration
• oscillatory
• infinite integrals
• Bessel function
• error analysis

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65D32
• 65D30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by Natural Science Foundation of Guangdong Province, China (No. 2015A030313615).