Fully discrete two-step mixed element method for the symmetric regularized long wave equation

A numerical method based on the explicit two-step method in time direction and the mixed finite element method in spatial direction is presented for the symmetric regularized long wave (SRLW) equation. The optimal a priori error estimates (O((Delta t)(2) + h(m+1) + h(k+1))) for fully discrete explicit two-step mixed scheme are derived. Moreover, a numerical example is provided to confirm our theoretical results.