Obregon, M. A. and Stepanyants, Y. A.
(2012)
*On numerical solution of the Gardner Ostrovsky equation.*
Mathematical Modelling of Natural Phenomena, 7 (2).
pp. 113-130.
ISSN 0973-5348

Text (Published Version)
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## 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.

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Item Type: | Article (Commonwealth Reporting Category C) |
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Refereed: | Yes |

Item Status: | Live Archive |

Additional Information (displayed to public): | Published Version deposited in accordance with copyright policy of publisher. |

Depositing User: | Assoc Prof Yury Stepanyants |

Faculty / Department / School: | Historic - Faculty of Sciences - Department of Maths and Computing |

Date Deposited: | 09 Oct 2012 11:02 |

Last Modified: | 11 Feb 2015 05:28 |

Uncontrolled Keywords: | KdV equation; Ostrovsky equation; solution; terminal decay; Petviashvili method; numerical scheme |

Fields of Research (FoR): | 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations 01 Mathematical Sciences > 0105 Mathematical Physics > 010599 Mathematical Physics not elsewhere classified 01 Mathematical Sciences > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified |

Socio-Economic Objective (SEO): | E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences |

Identification Number or DOI: | doi: 10.1051/mmnp/20127210 |

URI: | http://eprints.usq.edu.au/id/eprint/21212 |

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