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Best difference equation 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, 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
Information
The ANZIAM Journal , Volume 23 , Issue 4 , April 1982 , pp. 349 - 356
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), 64–77.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