This paper presents decoupled second-order accurate algorithms based on
Crank-Nicolson LeapFrog (CNLF) scheme for the evolution Boussinesq
equations. The proposed algorithms deal with the spatial discretization
by finite element method and treat the temporal discretization by CNLF
method. For the nonlinear term in the Boussinesq equations, the
semi-implicit method is used. Unconditional stability and error estimate
of the numerical algorithm are proven. Some numerical tests are
presented to justify the theoretical analysis.