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Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves. (English) Zbl 1480.76164

Summary: 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.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76M20 Finite difference methods applied to problems in fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
26A33 Fractional derivatives and integrals
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