Numerical study of Rosenau-KdV equation using finite element method based on collocation approach. (English) Zbl 1488.35474

Summary: In the present paper, a numerical method is proposed for the numerical solution of Rosenau-KdV equation with appropriate initial and boundary conditions by using collocation method with septic B-spline functions on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To check accuracy of the error norms \(L_2\) and \(L_{\infty}\) are computed. Interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves during the interaction. Furthermore, evolution of solitons is illustrated by undular bore initial condition. These results show that the technique introduced here is suitable to investigate behaviors of shallow water waves.


35Q53 KdV equations (Korteweg-de Vries equations)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M10 Finite element methods applied to problems in fluid mechanics
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
41A15 Spline approximation
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