Numerical analysis of a Family of Second Order Time Stepping Methods for Boussinesq Equations

—This report considers a family of second order time stepping schemes for Boussinesq system. The scheme uses the idea of curvature stabilization in which the discrete curvature of the solutions is added together with the linearized advective term at each time step. Unconditional stability and convergence of the method are established. Several numerical experiments are provided to demonstrate the accuracy and the efficiency of the method