Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-29T14:48:43.336Z Has data issue: false hasContentIssue false

A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations

Published online by Cambridge University Press:  24 October 2008

F. W. J. Olver
Affiliation:
National Physical LaboratoryTeddington, Middlesex

Extract

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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1950

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bickley, W. G., Miller, J. C. P. and Jones, C. W.Notes on the evaluation of zeros and turning values of Bessel functions. Phil. Mag. 36 (1945), 121–33 and 200–10.Google Scholar
(2)Milne-Thomson, L. M.Calculus of finite differences (Macmillan, 1933).Google Scholar
(3)Fox, L. and Goodwin, E. T.Some new methods for the numerical integration of ordinary differential equations. Proc. Cambridge Phil. Soc. 45 (1949), 373–88.Google Scholar
(4)Watson, G. N.Theory of Bessel functions (Cambridge, 1944).Google Scholar
(5)Bickley, W. G.Formulae relating to Bessel functions of moderate or large argument and order. Phil. Mag. 34 (1943), 371–49.CrossRefGoogle Scholar