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Exact solution of a difference approximation to Duffing's equation

Published online by Cambridge University Press:  17 February 2009

Renfrey B. Potts
Renfrey B. Potts
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia 5001
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Abstract

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Duffing's equation, in its simplest form, can be approximated by various non-linear difference equations. It is shown that a particular choice can be solved in closed form giving periodic solutions.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 1 , July 1981 , pp. 64 - 77
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Abramowitz, M. and Stegun, I. A. (ed.), Handbook of mathematical functions (U. S. National Bureau of Standards, 1964).Google Scholar
[2]Eminhizer, C. R., Helleman, R. H. G. and Montroll, E. W., “On a convergent nonlinear perturbation theory without small denominators or secular terms”, J. Math. Phys. 17 (1976), 121–140.CrossRefGoogle Scholar
[3]McLacMan, N. W., Ordinary non-linear differential equations in engineering and physical sciences (Oxford University Press 2nd edition, 1956), Chapter III.Google Scholar