In this interesting paper, an efficient method for locating , isolating and computing real zeros of Bessel functions is developed. The algorithm degree-isolate is developed to calculate the total number of real roots of Bessel functions within a pre-determined interval as also to isolate one of them. This procedure can be repeated for the isolation of each one of the zeros in this interval . Once a zero is isolated, the algorithm compute-zero is developed to compute it to any accuracy. Also, for any given interval
containing a single zero of a Bessel function, lower and upper bounds for this zero can be determined. The number of zeros of Bessel functions of various orders
existing within some given interval
, as well as the respective sub-intervals
, where exactly one root exists are presented here. Also, ten zeros of several Bessel functions, chosen at random, are given.