English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We deal with an initial-boundary value problem for the generalizedtime-dependent Schr\"odinger equation with variable coefficients in anunbounded $n$--dimensional parallelepiped ($n\geq 1$). To solve it, theCrank-Nicolson in time and the polylinear finite element in space method withthe discrete transpa\-rent boundary conditions is considered. We present itsstability properties and derive new error estimates $O(\tau^2+|h|^2)$ uniformlyin time in $L^2$ space norm, for $n\geq 1$, and mesh $H^1$ space norm, for$1\leq n\leq 3$ (a superconvergence result), under the Sobolev-type assumptionson the initial function. Such estimates are proved for methods with thediscrete TBCs for the first time.

On Error Estimates of the Crank-Nicolson-Polylinear Finite Element  Method with the Discrete TBC for the Generalized Schr\"odinger Equation in an  Unbounded Parallelepiped