Computers & Mathematics with Applications
The use of compact boundary value method for the solution of two-dimensional Schrödinger equation
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
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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) Schrödinger 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.