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Numerical computation of the time non-linear fractional generalized equal width model arising in shallow water channel

Can Nguyen Huu (Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)
Nikan Omid (Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)
Rasoulizadeh Mohammad Navaz (Department of Mathematics, Faculty of Basic Sciences, Velayat University, Iranshar, Iran)
Jafari Hossein (Institute of Research and Development, Duy Tan University, Da Nang, Vietnam + Department of Mathematical Sciences, University of South Africa, UNISA, Pretoria, South Africa), [email protected]
Gasimov Yusif S. (Azerbaijan University, Baku, Azerbaijan + Institute of Mathematics and Mechanics, ANAS, Baku, Azerbaijan + Institute for Physical Problems, Baku State University, Baku, Azerbaijan)

The generalized equal width model is an important non-linear dispersive wave model which is naturally used to describe physical situations in a water channel. In this work, we implement the idea of the interpolation by radial basis function to obtain numerical solution of the non-linear time fractional generalized equal width model defined by Caputo sense. In this technique, firstly, a time discretization is accomplished via the finite difference approach and the non-linear term is linearized by a linearization method. Afterwards, with the help of the radial basis function approximation method is used to discretize the spatial derivative terms. The stability of the method is theoretically discussed using the von Neumann (Fourier series) method. Numerical results and comparisons are presented which illustrate the validity and accuracy of our proposed concepts.

Keywords: non-linear time fractional generalized equal width model, stability, radial basis function-finite difference, Caputo fractional derivative