A second-order Fourier pseudospectral method for the generalized regularized long wave equation.

We present a second-order in time linearized semi-implicit Fourier pseudospectral scheme for the generalized regularized long wave equation. Based on the consistency analysis, the nonlinear stability and the convergence of the scheme are discussed, along with the a priori assumption and an aliasing error control estimate. The numerical examples demonstrate the features of the proposed scheme, including the convergence order, conservative properties, and the evolution of the unstable wave. [ABSTRACT FROM AUTHOR]