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- W2000456788 abstract "We investigate numerical techniques for the solution of the time-dependent Schrodinger equation in one and two space dimensions. We introduce a framework for constructing finite difference schemes based on Pade approximations for both the time and space discretization and apply this framework to construct high order finite difference schemes for Schrodinger's equation in conjunction with an operator splitting approach. We also discuss three level schemes as an alternative to operator splitting.The accuracy and stability of these methods is studied, and their efficiencies are compared. The results of some numerical comparisons of the methods are presented.For two space dimensions, some of the new techniques proposed include a split-step Crank-Nicolson scheme, where the implicit equations at each time step can be solved by a fast Poisson solver. The two-dimensional methods have ADI (alternating direction implicit) analogues which reduce the complexity of the computations.We describe how a balanced form of cyclic reduction and a method that exploits the transpose operation on hypercubes lead to effective strategies for parallelizing the solution of multiple tridiagonal equations that arise in the solution of the Schrodinger equation in two space dimensions in the ADI approach. We show that in spite of the implicit nature of these schemes, they can be parallelized with high efficiencies on MIMD hypercubes." @default.
- W2000456788 created "2016-06-24" @default.
- W2000456788 creator A5061288959 @default.
- W2000456788 date "1991-05-01" @default.
- W2000456788 modified "2023-09-27" @default.
- W2000456788 title "Numerical techniques for the solution of the time-dependent Schrodinger equation and their parallel implementation" @default.
- W2000456788 hasPublicationYear "1991" @default.
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