A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions

被引：1

作者：

Slevinsky, Richard M. ^{[1
]}

Safouhi, Hassan ^{[2
]}

机构：

[1] Univ Manitoba, Dept Math, 186 Dysart Rd, Winnipeg, MB R3T 2M8, Canada

[2] Univ Alberta, Campus St Jean,8406,91 St, Edmonton, AB T6C 4G9, Canada

来源：

NUMERICAL ALGORITHMS | 2023年 / 92卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Incomplete Bessel functions; Extrapolation methods; The G transformation; Numerical integration; The Slevinsky-Safouhi formulae; AQUIFER; INTEGRALS; FORMULA;

D O I：

10.1007/s11075-022-01438-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the G(n)((1)) transformation and Slevinsky-Safouhi formula for differentiation. In the present contribution, we improve this existing algorithm for incomplete Bessel functions by developing a recurrence relation for the numerator sequence and the denominator sequence whose ratio forms the sequence of approximations. By finding this recurrence relation, we reduce the complexity from O(n(4)) to O(n). We plot relative error showing that the algorithm is capable of extremely high accuracy for incomplete Bessel functions.

引用

页码：973 / 983

页数：11

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