Adaptive Absorbing Boundary Conditions for Schrödinger-type Equations

Conference paper

Abstract

Let us consider the Schrödinger-type equation given by
$$ \partial _t u(x,t) = \frac{{ - i}} {c}(\partial _{xx} u(x,t) + Vu(x,t)),\quad x \in R,\quad t \in 0 $$
(1)
with c > 0. In order to obtain a numerical solution of the initial value problem for this equation, it is essential to consider a finite spatial subdomain [x l , x r ] and to use artificial boundary conditions. One option is to develop local absorbing boundary conditions (ABC) that allow only small reflections of the solution and are constructed by approximating the transparent or reflection-free boundary conditions (TBC) which are nonlocal.

Keywords

Microwave Lution 

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Universidad de ValladolidSpain
  2. 2.Universidad de BurgosSpain

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