The finite difference approximations of the optimal control problem for non-linear Schrodinger equation

摘要

In this paper, the finite difference method is applied to the optimal control problem of system governed by non-linear Schrodinger equation. For this purpose, the finite difference scheme is constituted for considered optimal control problem. Obtained an estimation for the solution of this difference scheme, the error of the difference scheme is evaluated. Finally, the convergence according to the functional of the finite difference approximations is proved.