Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T07:23:22.494Z Has data issue: false hasContentIssue false
  • English
  • Français

On the non-linear difference equation Δxn = kΦ (xn)

Published online by Cambridge University Press:  24 October 2008

J. B. S. Haldane
J. B. S. Haldane
Affiliation:
Trinity College
Get access Rights & Permissions [Opens in a new window]

Extract

1. Among the equations arising in the theory of natural selection is the finite difference equation

where k is a constant which may have any value between 1 and − ∞ inclusive, but is often small. Its solution is discussed in the accompanying paper(1). It is a particular case of the equation

where Φ(x) is a known one-valued function of x. When k is small this may obviously be solved approximately by treating it as a differential equation

whence

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 2 , April 1932 , pp. 234 - 243
Copyright
Copyright © Cambridge Philosophical Society 1932

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)Haldane, , Proc. Camb. Phil. Soc., 28 (1932).Google Scholar
(2)Steffensen, , Interpolation, London, 1927.Google Scholar
(3)Fisher, , Proc. Roy. Soc. Edin. 50, p. 204 (1930).CrossRefGoogle Scholar