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Zbl 0915.33001
Vrahatis, M.N.; Grapsa, T.N.; Ragos, O.; Zafiropoulos, F.A.
On the localization and computation of zeros of Bessel functions. (English)
[J] Z. Angew. Math. Mech. 77, No.6, 467-475 (1997); correction ibid. 79, No.2, 144-145 (1999). ISSN 0044-2267; ISSN 0946-8463/e

In this interesting paper, an efficient method for locating , isolating and computing real zeros of Bessel functions is developed. The algorithm degree-isolate is developed to calculate the total number of real roots of Bessel functions within a pre-determined interval as also to isolate one of them. This procedure can be repeated for the isolation of each one of the zeros in this interval . Once a zero is isolated, the algorithm compute-zero is developed to compute it to any accuracy. Also, for any given interval $(a_k,b_k)$ containing a single zero of a Bessel function, lower and upper bounds for this zero can be determined. The number of zeros of Bessel functions of various orders $\nu$ existing within some given interval $(a,b)$, as well as the respective sub-intervals $(a_k,b_k)$, where exactly one root exists are presented here. Also, ten zeros of several Bessel functions, chosen at random, are given.
[C.L.Koul (Jaipur)]

MSC 2000:: *33C10 Cylinder functions, etc.
65D20 Computation of special functions
34B30 Special ODE

Keywords: localization of zeros of functions; topological degree; isolation of zeros of Bessel functions

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