A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations
- 24 October 1950
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 46 (4) , 570-580
- https://doi.org/10.1017/s030500410002613x
Abstract
The zeros of solutions of the general second-order homogeneous linear differential equation are shown to satisfy a certain non-linear differential equation. The method here proposed for their determination is the numerical integration of this differential equation. It has the advantage of being independent of tabulated values of the actual functions whose zeros are being sought. As an example of the application of the method the Bessel functions Jn(x), Yn(x) are considered. Numerical techniques for integrating the differential equation for the zeros of these Bessel functions are described in detail.This publication has 3 references indexed in Scilit:
- Some new methods for the numerical integration of ordinary differential equationsMathematical Proceedings of the Cambridge Philosophical Society, 1949
- XXIII. Notes on the evaluation of zeros and turning values of Bessel functions.—IV. A new expansionJournal of Computers in Education, 1945
- V. Formulæ relating to Bessel functions of moderate or large argument and orderJournal of Computers in Education, 1943