文献类型：期刊文献

英文题名：Unified steepest-descent quadrature for oscillatory -fold Bessel product integrals via frequency-aware Hankel splitting

作者：Zhang, Jian[1];Du, Hong[1]

机构：[1]Guangdong Ocean Univ, Coll Math & Comp Sci, Zhanjiang 524088, Guangdong, Peoples R China

年份：2026

卷号：72

期号：7

外文期刊名：JOURNAL OF APPLIED MATHEMATICS AND COMPUTING

收录：SCI-EXPANDED(收录号：WOS:001812842700004)、、EI(收录号：20262821059667)、Scopus(收录号：2-s2.0-105043919113)、WOS

基金：No funding was received to assist with the preparation of this manuscript.

语种：英文

外文关键词：Oscillatory quadrature; Multi-bessel product integrals; Steepest-descent contour deformation; Hankel splitting; Adaptive frequency-aware partitioning

外文摘要：A unified quadrature framework is developed for highly oscillatory integrals involving general -fold products of Bessel functions on finite and semi-infinite intervals. The framework is intended for difficult regimes, including equal or nearly equal frequencies, algebraic endpoint behavior, and large Bessel orders. The method combines a left-end expansion, a selective Hankel splitting applied only to strongly oscillatory factors, and a unified steepest-descent quadrature operator. The operator uses Gauss-Legendre (GL) rules on short real segments and Gauss-Laguerre (GLag) rules on deformed rays. A split-merge strategy further reduces the number of subintegrals while preserving frequency awareness. The factor is handled directly, without desingularization. Separate bounds are given for the left-end truncation, finite-segment quadrature, vertical-ray quadrature, and tail contribution. These component bounds lead to an additive global error estimate and stability bounds for the composite scheme. Numerical experiments show exponential-type error decay with few nodes, robust behavior in equal-frequency and large-order regimes, and competitive cost-accuracy performance in the reported tests.