Symplectic scheme in computing the one-dimensional model of strong laser field

The symplectic algorithm of Hamiltonian system is extended to the complex symplectic space. The numerical solutions of the 1-dimensional model of strong field are calculated by means of both symplectic and Runge-Kutta algorithms. The results show that the symplectical gorithm preserves the Wronskian, which is in good agreement with theoretical analyses, but the Wronskian calculated by using the Runge-Kutta algorithm increases rapidly after a long distance of computation. Therefore the symplectic algorit hm is a better algorithm for the calculations of the 1-dimensional model of strong field.