On numerical solution of the Gardner Ostrovsky equation
Article
Article Title | On numerical solution of the Gardner Ostrovsky equation |
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ERA Journal ID | 32402 |
Article Category | Article |
Authors | Obregon, M. A. (Author) and Stepanyants, Y. A. (Author) |
Journal Title | Mathematical Modelling of Natural Phenomena (MMNP) |
Journal Citation | 7 (2), pp. 113-130 |
Number of Pages | 18 |
Year | 2012 |
Place of Publication | Les Ulis, France |
ISSN | 0973-5348 |
1760-6101 | |
Digital Object Identifier (DOI) | https://doi.org/10.1051/mmnp/20127210 |
Web Address (URL) | http://www.mmnp-journal.org/action/displayAbstract?fromPage=online&aid=8503520 |
Abstract | A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky equation which is also known as the extended rotation-modified Korteweg–de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth' rotation. Particular versions of this equation are also known in numerous applications. The proposed numerical scheme is a further development of the well-known finite-difference scheme earlier used for the solution of the KdV equation. The scheme is of the second order accuracy both on temporal and spatial variables. The stability analysis of the scheme is presented for infinitesimal perturbations. The conditions for the calculations with the appropriate accuracy have been found. Examples of calculations with the periodic boundary conditions are presented to illustrate the robustness of the proposed scheme. |
Keywords | KdV equation; Ostrovsky equation; solution; terminal decay; Petviashvili method; numerical scheme |
ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |
490299. Mathematical physics not elsewhere classified | |
490199. Applied mathematics not elsewhere classified | |
Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
Byline Affiliations | University of Malaga, Spain |
Department of Mathematics and Computing | |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q1492/on-numerical-solution-of-the-gardner-ostrovsky-equation
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