On quadrature of highly oscillatory Bessel function via asymptotic analysis of simplex integrals

被引:0
作者
Zhou, Yongxiong [1 ]
Chen, Ruyun [1 ]
机构
[1] Guangdong Ocean Univ, Fac Math & Comp Sci, Zhanjiang 524088, Peoples R China
关键词
Bessel function; Quadrature; Asymptotic expansion; Laplace transform; COMPUTATION; TRANSFORMS;
D O I
10.1016/j.cam.2024.116239
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, two methods for evaluating highly oscillatory Bessel integrals are explored. Firstly, a polynomial is analyzed as an effective approximation of the simplex integral of a highly oscillatory Bessel function based on Laplace transform, and its error rapidly decreases as the frequency increases. Furthermore, the inner product of f and highly oscillatory Bessel function can be approximated by two other forms of inner product by which one depends on a polynomial and the higher derivatives of f , another depends on Bessel function and the interpolation polynomial of f . In addition, three issues related to highly oscillatory Bessel integrals have also been discussed: inequalities for the convergence rate of Filontype methods, evaluation of Cauchy principal values, and simplified evaluation on infinite intervals. Through some preliminary numerical experiments, our theoretical analysis has been preliminarily confirmed, and the proposed numerical method is accurate and effective.
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页数:18
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