A dissipative finite difference Fourier pseudo-spectral method for the symmetric regularized long wave equation with damping mechanism

In this paper, an energy stable time-stepping method using the finite difference approximation in time and Fourier pseudo-spectral method in space is developed for the symmetric regularized long wave equation with damping mechanism. Based upon a careful treatment of nonlinear term, the suggested numerical scheme is proved to preserve energy dissipation at discrete time levels. The energy stable property implies the priori estimates of the numerical solution. The maximum norm error estimate shows that the proposed numerical scheme is of second-order accuracy in time and spectral accuracy in space. Several numerical experiments are presented to show the effectiveness of our numerical method and to confirm our theoretical analysis.