Two discretisations of the Ermakov-Pinney equation

Common, A.K. and Musette, M. (1997) Two discretisations of the Ermakov-Pinney equation. Physics Letters A, 235 (6). pp. 574-580. ISSN 0375-9601. (The full text of this publication is not available from this repository)

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Abstract

We propose two candidates for discrete analogues to the nonlinear Ermakov-Pinney equation. The first one based on an association with a two-dimensional conformal mapping defines a second-degree difference scheme. It possesses the same features as in the continuum: a nonlinear superposition principle relating its general solution to a second-order linear difference equation and by direct linearisation a relationship with a third-order difference equation. The second form, which is new, is obtained from a slight improvement of the superposition principle. It has the advantage of leading to a first degree difference scheme and preserves all the nice properties of its linearisation. (C) 1997 Elsevier Science B.V.

Item Type: Article
Depositing User: T. Nasir
Date Deposited: 25 Oct 2009 09:35
Last Modified: 25 Oct 2009 09:35
Resource URI: http://kar.kent.ac.uk/id/eprint/18360 (The current URI for this page, for reference purposes)
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