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

2022/04/24 by Richard Mikaël Slevinsky, Slevinsky, Richard M., Hassan Safouhi +1 · 1 citation
Mathematics · Physics and Astronomy · #65B05 #65D30 #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2204.11197

openalex publication_date 2022/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \cal O(n⁴) to \cal O(n). We plot relative error showing that the algorithm is capable of extremely high accuracy for incomplete Bessel functions.

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