Numerical solution of Boussinesq equations as a model of interfacial-wave propagation.
Wiryanto, L.H. (2005)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Wiryanto, L.H. (2005)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Manuel G. Velarde (1993)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Zhou, Jiangbo, Tian, Lixin (2009)
Mathematical Problems in Engineering
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Bhatti, Zahid Rafiq, Durrani, Ijaz-Ur-Rahman (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Gera, Dinesh, Gautam, Mridul, Gangarao, Hota V.S. (1997)
International Journal of Mathematics and Mathematical Sciences
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Pudjaprasetya, S.R., Chendra, H.D. (2009)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Feng, Bao-Feng (2004)
International Journal of Mathematics and Mathematical Sciences
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Khader, M.M., Al-Bar, R.F. (2011)
Mathematical Problems in Engineering
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Vlastislav Červený, Jaromír Janský (1967)
Acta Universitatis Carolinae. Mathematica et Physica
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Stéphane Labbé, Lionel Paumond (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study...
Anna Karczewska, Piotr Rozmej, Maciej Szczeciński, Bartosz Boguniewicz (2016)
International Journal of Applied Mathematics and Computer Science
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The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic...