Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{O}(\delta t^{2-\alpha}) $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M2">\begin{document}$ 0 &lt; \alpha&lt; 1 $\end{document}</tex-math></inline-formula> 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.</p>