A semi-discrete higher order compact scheme for the unsteady two-dimensional Schrödinger 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) Schrödinger equation. The scheme is second order accurate in time and fourth order accurate in space. The r...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2006-12, Vol.197 (1), p.141-149
Main Authors: Kalita, Jiten C., Chhabra, Puneet, Kumar, Sudhanshu
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
High accuracy
HOC
Implicit
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Schrödinger equation
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.10.032