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Home / Journal of Computational and Theoretical Nanoscience, Volume 13, Number 10

Numerical Scheme to Dispersive Shallow Water Waves

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This paper studies dispersive shallow water waves modeled by Rosenau Korteweg-de Vries (KdV) Regularized long wave (RLW) equation or R-KdV-RLW equation that is considered with power law nonlinearity. The numerical algorithm is based on collocation finite element method with quintic B-splines. Test problems including the motion of solitary waves and shock waves are studied to validate the suggested method. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and error norms L 2 and L ∞. A linear stability analysis based on a Fourier method shows that the numerical scheme is unconditionally stable.

Keywords: Collocation; Dispersion; Finite Element; R-KdV-RLW Equation; Shallow Water; Solitary Waves; Solitons

Document Type: Research Article

Affiliations: 1: Department of Transportation Engineering, Faculty of Engineering, Yalova University, 77100 Yalova, Turkey 2: Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University, 50300 Nevsehir, Turkey 3: Department of Mathematical Sciences, Delaware State University Dover, DE 19901-2277, USA

Publication date: 01 October 2016

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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