New method of oscillatory integrals involving two Bessel functions

Hong Du; Zhong Chen

doi:10.1016/j.amc.2025.129906

New method of oscillatory integrals involving two Bessel functions

Hong Du
, Zhong Chen^*

^*Corresponding author for this work

Guangdong Ocean University
Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

Abstract

New method based on numerical steepest descent method (NSDM) is proposed for highly oscillatory integrals (HOIs) with products of two Bessel functions on [a, b]. The calculation of the HOIs is provided for the two cases a > 0 and a=0. Especially under Case a=0, the recurrence relation of moment functions is obtained, the key calculation of four moment functions of degree 0 is solved using the NSDM and the stability of the recurrence relation is also analyzed. Two numerical tests verified the effectiveness of the proposed method.

Original language	English
Article number	129906
Journal	Applied Mathematics and Computation
Volume	519
DOIs	https://doi.org/10.1016/j.amc.2025.129906
State	Published - 15 Jun 2026
Externally published	Yes

Keywords

33C10
65R10
Bessel function
Numerical steepest descent method 2020 MSC 65D30
Oscillatory integrals

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10.1016/j.amc.2025.129906

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title = "New method of oscillatory integrals involving two Bessel functions",

abstract = "New method based on numerical steepest descent method (NSDM) is proposed for highly oscillatory integrals (HOIs) with products of two Bessel functions on [a, b]. The calculation of the HOIs is provided for the two cases a > 0 and a=0. Especially under Case a=0, the recurrence relation of moment functions is obtained, the key calculation of four moment functions of degree 0 is solved using the NSDM and the stability of the recurrence relation is also analyzed. Two numerical tests verified the effectiveness of the proposed method.",

keywords = "33C10, 65R10, Bessel function, Numerical steepest descent method 2020 MSC 65D30, Oscillatory integrals",

author = "Hong Du and Zhong Chen",

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year = "2026",

month = jun,

day = "15",

doi = "10.1016/j.amc.2025.129906",

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T1 - New method of oscillatory integrals involving two Bessel functions

AU - Du, Hong

AU - Chen, Zhong

PY - 2026/6/15

Y1 - 2026/6/15

N2 - New method based on numerical steepest descent method (NSDM) is proposed for highly oscillatory integrals (HOIs) with products of two Bessel functions on [a, b]. The calculation of the HOIs is provided for the two cases a > 0 and a=0. Especially under Case a=0, the recurrence relation of moment functions is obtained, the key calculation of four moment functions of degree 0 is solved using the NSDM and the stability of the recurrence relation is also analyzed. Two numerical tests verified the effectiveness of the proposed method.

AB - New method based on numerical steepest descent method (NSDM) is proposed for highly oscillatory integrals (HOIs) with products of two Bessel functions on [a, b]. The calculation of the HOIs is provided for the two cases a > 0 and a=0. Especially under Case a=0, the recurrence relation of moment functions is obtained, the key calculation of four moment functions of degree 0 is solved using the NSDM and the stability of the recurrence relation is also analyzed. Two numerical tests verified the effectiveness of the proposed method.

KW - 33C10

KW - 65R10

KW - Bessel function

KW - Numerical steepest descent method 2020 MSC 65D30

KW - Oscillatory integrals

UR - https://www.scopus.com/pages/publications/105026138372

U2 - 10.1016/j.amc.2025.129906

DO - 10.1016/j.amc.2025.129906

M3 - 文章

AN - SCOPUS:105026138372

SN - 0096-3003

VL - 519

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 129906

ER -

New method of oscillatory integrals involving two Bessel functions

Abstract

Keywords

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