Obregon, M. and Raj, N. ORCID: https://orcid.org/0000-0002-8364-2644 and Stepanyants, Y.
ORCID: https://orcid.org/0000-0003-4546-0310
(2012)
Numerical study of nonlinear wave processes by means of discrete chain models.
In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.
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Abstract
We show that many nonlinear wave processes in dispersive and dissipative media can be numerically studied by means of chain models describable by sets of ODEs. This allows us to obtain higher accuracy results for relatively cheap price using standard ODE-solvers. The advantages of this approach in comparison with the direct numerical modeling of PDEs are: (i) the chain model has a vivid physical meaning and can be created in a laboratory in various embodiments playing a role of analogous computers; (ii) there is no need to develop a complex numerical scheme and study its stability and convergence. We demonstrate the idea in application to the modeling of solitary wave propagation in a rotating ocean described by the Gardner–Ostrovsky PDE using a modified Toda chain model. We show that our results are in a good agreement with approximate theoretical findings and early published data obtained from the direct numerical modeling of the Gardner–Ostrovsky PDE.
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