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Preprint 22-2006

Discrete Transparent Boundary Conditions for Schrödinger-type equations for non-compactly supported initial data

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Postscript Document

Author(s) : Matthias Ehrhardt

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 22-2006

MSC 2000

65M06 Finite difference methods
35Q40 Equations from quantum mechanics

PACS : 02.70.Bf, 31.15.Fx

Abstract :
Transparent boundary conditions (TBCs) are an important tool for the truncation of the computational domain in order to compute solutions on an unbounded domain. In this work we want to show how the standard assumption of `compactly supported data' could be relaxed and derive TBCs for a generalized Schrödinger equation directly for the numerical scheme on the discrete level. With this inhomogeneous TBCs it is not necessary that the initial data lies completely inside the computational region. However, an increased computational effort must be accepted.

Keywords : Schrödinger-type equation, transparent boundary condition, unbounded domain, non-compactly supported initial data, finite differences

Notes :
submitted to: Applied Numerical Mathematics

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