Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves
O. Nikan, Seyedeh Mahboubeh Molavi-Arabshai, Hossein Jafari
Abstract
This paper aimed at obtaining the traveling-wave solution of the nonlinear time fractional regularized long-wave equation. In this approach, firstly, the time fractional derivative is accomplished using a finite difference with convergence order $ \mathcal{O}(\delta t^{2-\alpha}) $ for $ 0 < \alpha< 1 $ and the nonlinear term is linearized by a linearization technique. Then, the spatial terms are approximated with the help of the radial basis function (RBF). Numerical stability of the method is analyzed by applying the Von-Neumann linear stability analysis. Three invariant quantities corresponding to mass, momentum and energy are evaluated for further validation. Numerical results demonstrate the accuracy and validity of the proposed method.