Finite Element Method for Stochastic Extended KdV Equations

Karczewska Anna 1*, Szczeciński Maciej 1, Rozmej Piotr 2**, Boguniewicz Bartosz 2

1 Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra, Poland
∗E-mail: a.karczewska@wmie.uz.zgora.pl

2 Faculty of Physics and Astronomy, Institute of Physics University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra, Poland
∗∗E-mail: p.rozmej@if.uz.zgora.pl

Received:

Received: 12 September 2015; revised: 26 January 2016; accepted: 29 January 2016; published online: 16 March 2016

DOI:   10.12921/cmst.2016.22.01.002

Abstract:

The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves under stochastic forces are presented. Though small effects originating from second order dynamics may be obscured by stochastic forces, the main waves, both cnoidal and solitary ones, remain very robust against any distortions.

Key words:

nonlinear equations, second order KdV equations, shallow water wave problem, stochastic forces

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