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Continuous symmetries of the discrete nonlinear telegraph equation

Published online by Cambridge University Press:  01 June 1999

M. S. ODY ,
A. K. COMMON  and
M. I. SOBHY
M. S. ODY
Affiliation:
Institute of Mathematics and Statistics, University of Kent at Canterbury, Kent CT2 7NF, UK Electronic Engineering Laboratories, University of Kent at Canterbury, Kent CT2 7NT, UK
A. K. COMMON
Affiliation:
Institute of Mathematics and Statistics, University of Kent at Canterbury, Kent CT2 7NF, UK
M. I. SOBHY
Affiliation:
Electronic Engineering Laboratories, University of Kent at Canterbury, Kent CT2 7NT, UK
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Abstract

The method of classical Lie symmetries, generalised to differential-difference equations by Quispel, Capel and Sahadevan, is applied to the discrete nonlinear telegraph equation. The symmetry reductions thus obtained are compared with analogous results for the continuous telegraph equation. Some of these ‘continuous’ reductions are used to provide initial data for a numerical scheme which attempts to solve the corresponding discrete equation.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 10 , Issue 3 , June 1999 , pp. 265 - 284
Copyright
1999 Cambridge University Press

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