Discrete transparent boundary conditions for Schrodinger-type equations for non-compactly supported initial data

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 Schrodinger 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. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.