Abstract
When a partial differential equation in an unbounded domain is solved numerically, it is necessary to introduce artificial boundary conditions. In this paper, a general class of absorbing boundary conditions is constructed for one-dimensional Schrödinger-type equations discretized in space by finite differences. For this, rational approximations to the transparent boundary conditions are used. We study the simplest case in detail, obtaining an estimate for the full discrete error and showing that the discrete problem is weakly unstable. Moreover, we show numerically that the discrete problems associated to higher order absorbing boundary conditions are more unstable. Several numerical experiments confirm the results previously obtained.
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