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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
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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

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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