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On the computation of zeros of Bessel- and Bessel related functions. (English) Zbl 0882.34034
Bainov, D. (ed.), Proceedings of the sixth international colloquium on differential equations, Plovdiv, Bulgaria, August 18--23, 1995. Zeist: VSP. 409-416 (1996).
Summary: Topological degree theory is employed for the localization and isolation of zeros of Bessel, Airy and Coulomb functions. Specifically, Picard extension, Kronecker integral and Kearfott’s degree computation method are used for the calculation of the total number of these zeros in a predetermined region and for their isolation. Then, a modified bisection method is applied for the computation of these zeros, requiring only the algebraic signs of the considered function. Numerical examples are presented. For the entire collection see [Zbl 0870.00027].
34B30Special ODE (Mathieu, Hill, Bessel, etc.)
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$