Mn. Vrahatis et al., ON THE LOCALIZATION AND COMPUTATION OF ZEROS OF BESSEL-FUNCTIONS, Zeitschrift fur angewandte Mathematik und Mechanik, 77(6), 1997, pp. 467-475
The topological degree of a continuous mapping is implemented for the
calculation of the total number of the simple real zeros within any in
terval of the Bessel functions of first and second kind and their deri
vatives. A new algorithm, based on this implementation, is given for t
he localization and isolation of these zeros. Furthermore, a second al
gorithm is presented for their computation employing a modified bisect
ion method. The only information required for this computation is the
algebraic signs of function values. Moreover, lower and upper bounds o
f a zero can also be obtained.