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Greenspan’s harmonic oscillator

Published online by Cambridge University Press:  22 September 2016

J. Astin*
Affiliation:
University College of Wales, Aberystwyth, Dyfed SY23 3BZ

Extract

In a recently published book by Greenspan classical dynamics is modelled by a set of difference equations. There are two distinct reasons why this approach could be useful. First, since all our measurements are made at specific times and are thus not continuous it may be that the model is a “better” representation than the usual one using the calculus. Secondly, since most practical problems are now solved by numerical techniques, and one of the most used of these is the method of finite difference, a formulation of the basic equations in difference form makes them directly amenable to numerical solution. There are numerous ways of modelling the derivatives as differences and Greenspan chooses a way which preserves the energy equation. This is aesthetically pleasing and also gives rise generally to stable numerical schemes.

Type
Research Article
Copyright
Copyright © Mathematical Association 1981

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References

Greenspan, D., Arithmetic applied mathematics. Pergamon Press, Oxford (1980).Google Scholar