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Best difference equation approximation to Duffing's equation

Published online by Cambridge University Press:  17 February 2009

Renfrey B. Potts
Affiliation:
Department of Applied Mathematics, University of Adelaide, G.P.O. Box 498, Adelaide, South Australia 5001
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Abstract

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Duffing's differential equation in its simplest form can be approximated by a variety of difference equations. It is shown how to choose a ‘best’ difference equation in the sense that the solutions of this difference equation are successive discrete exact values of the solution of the differential equation.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Abramowitz, M. and Stegun, I. A. (eds.), Handbook of mathematical functions (U.S. National Bureau of Standards, Washington, D. C., 1964).Google Scholar
[2]McLachlan, N. W., Ordinary non-linear differential equations in engineering and physical sciences (Oxford University Press 2nd edition, 1956), Chapter III.Google Scholar
[3]Potts, R. B., “Exact solution of a difference approximation to Duffing's equation”, J. Anstral. Math. Soc. B 23 (1981), 6477.CrossRefGoogle Scholar
[4]Potts, R. B., “Differential and difference equations”, (in press).Google Scholar
[5]Potts, R. B., “Non-linear difference equations”, (submitted for publication).Google Scholar