A semi-discrete higher order compact scheme for the unsteady two-dimensional Schrِdinger equation

In this study, an implicit semi-discrete higher order compact (HOC) scheme, with an averaged time discretization, has been presented for the numerical solution of unsteady two-dimensional (2D) Schrِdinger equation. The scheme is second order accurate in time and fourth order accurate in space. The results of numerical experiments are presented, and are compared with analytical solutions and well established numerical results of some other finite difference schemes. In all cases, the present scheme produces highly accurate results with much better computational efficiency.