RFSFNS: a portable package for the numerical determination of the number and the calculation of roots of Bessel functions. 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 ν (z), Y ν (z), respectively, and their derivatives, where ν≥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. (Source: http://cpc.cs.qub.ac.uk/summaries/)

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Vrahatis, Michael N.: Generalizations of the intermediate value theorem for approximating fixed points and zeros of continuous functions (2020)
  2. Pérez-Arancibia, Carlos; Durán, Mario: On the Green’s function for the Helmholtz operator in an impedance circular cylindrical waveguide (2010)
  3. Sheng, Daichao; Pedroso, Dorival M.; Abbo, Andrew J.: Non-convexity and stress-path dependency of unsaturated soil models (2008)
  4. Kavvadias, D. J.; Makri, F. S.; Vrahatis, M. N.: Efficiently computing many roots of a function (2005)
  5. Gil, Amparo; Segura, Javier: A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions (2003)
  6. Mourrain, B.; Vrahatis, M. N.; Yakoubsohn, J. C.: On the complexity of isolating real roots and computing with certainty the topological degree (2002)
  7. Plagianakos, V. P.; Nousis, N. K.; Vrahatis, M. N.: Locating and computing in parallel all the simple roots of special functions using PVM (2001)
  8. Segura, Javier: Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros (2001)
  9. Segura, J.; Gil, A.: ELF and GNOME: two tiny codes to evaluate the real zeros of the Bessel functions of the first kind for real orders (1999)
  10. Kravanja, P.; Cools, R.; Haegemans, A.: Computing zeros of analytic mappings: A logarithmic residue approach (1998)
  11. Kravanja, P.; Ragos, O.; Vrahatis, M. N.; Zafiropoulos, F. A.: ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument (1998)
  12. Vrahatis, M. N.; Ragos, O.; Skiniotis, T.; Zafiropoulos, F. A.; Grapsa, T. N.: RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions (1995)