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RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions. (English) Zbl 0908.65010
Summary: A portable software package, named RFSFNS, is presented for the localization and computation of the simple real zeros of the Bessel functions of first and second kind, $J_\nu(z)$, $Y_\nu(z)$, respectively, and their derivatives, where $\nu\ge 0$ and $z>0$. This package implements the topological degree theory for the localization portion and a modified bisection method for the computation one. It localizes, isolates and computes with certainty all the desired zeros of the above functions in a predetermined interval within any accuracy (subject to relative machine precision). It has been implemented and tested on different machines utilizing the above Bessel functions of various orders and several intervals of the argument.

65D20Computation of special functions, construction of tables
65Y15Packaged methods in numerical analysis
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
Full Text: DOI
[1] Vrahatis, M. N.; Ragos, O.; Zafiropoulos, F. A.; Grapsa, T. N.: Locating and computing zeros of Airy functions. Z. angew. Math. mech. 75, 9 (1995) · Zbl 0878.33001
[2] M.N. Vrahatis, T.N. Grapsa, O. Ragos and F.A. Zafirpoulos, On the localization and computation of zeros of Bessel functions, submitted. · Zbl 0915.33001
[3] M.N. Vrahatis, O. Ragos, T. Skiniotis, F.A. Zafiropoulos and T.N. Grapsa, Locating and computing complex zeros of Bessel functions, submitted. · Zbl 0892.33002
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