R68-38 Accurate Analog Computer Generation of Bessel Functions for Large Ranges

Abstract

In analog computation there is a tendency not only to strive for the highest possible accuracy, but very often the ciiterion for accepting an analog scheme also requires minimizing the number of computer components and the duration of the problem preparation time. On the other hand, in analog or hybrid computation every sophistication intended to improve accuracy usually calls for more computer equipment, and every sophistication introduced to reduce comptuter equipment usually requires more time for problem preparation. Having this in mind, the method of Bessel function generation, discussed in Bingulac and Humol (Reference 5 in Hausner's paper), may be considered as the first degree of sophistication, since in developing this method the only criterion was to reduce the complexity of the analog computer scheme, thereby decreasing the number of computer components. Van Remoartere's method, 2 however, represents the second degree of sophistication because a) it divides the whole range of the independent vatiable into two subintervals, and b) in the first subinterval it approximates the solution by a Taylor series. This of course improves the accuracy but on the other hand, the number of analog computer components increases.