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Regular version of the site

Article

Family of Finite-Difference Schemes with Transparent Boundary Conditions for the Nonstationary Schrodinger Equation in a Semi-Infinite Strip

Доклады Академии наук. 2011. Vol. 436. No. 1. P. 12-18.
A. Zlotnik, I. A. Zlotnik.

An initial–boundary value problem for the generalized Schrödinger equation in a semi-infinite strip is solved.

A new family of two level finite-difference schemes with averaging over spatial variables on a finite mesh is constructed, which covers a set of finite-difference schemes built using various methods. For the family, an abstract approximate transparent boundary condition (TBC) is formulated and the solutions are proved to be absolutely stable in two norms with respect to both initial data and free terms. A discrete TBC is derived, and the stability of the family of schemes with this TBC is proved. The implementation of schemes with the discrete TBC is discussed.