On the Localization and Computation of Zeros of Bessel Functions

The topological degree of a continuous mapping is implemented for the calculation of the total number of the simple real zeros within any interval of the Bessel functions of first and second kind and their derivatives. A new algorithm, based on this implementation, is given for the localization and isolation of these zeros. Furthermore, a second algorithm is presented for their computation employing a modified bisection method. The only information required for this computation is the algebraic signs of function values. Moreover, lower and upper bounds of a zero can also be obtained.

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