Numerical behaviour of stable and unstable solitary waves

Authors:
A. Durán;M. A. López-Marcos
Affiliations:
Departamento de Matemática Aplicada y Computación, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain;Departamento de Matemática Aplicada y Computación, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain
Venue:
Applied Numerical Mathematics
Year:
2002

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Abstract

In this paper we analyse the behaviour in time of the numerical approximations to solitary wave solutions of the generalized Benjamin-Bona-Mahony equation. This equation possesses an important property: the stability of these solutions depends on their velocity. We identify the error propagation mechanisms in both the stable and unstable case. In particular, we show that in the stable case, numerical methods that preserve some conserved quantities of the problem are more appropriate for the simulation of this kind of solutions.