This article is cited in 1 paper

On the stability of the $\sigma$-scheme with transparent boundary conditions for parabolic equations

A. A. Zlotnik

Department of Applied Mathematics, Russian State Social University, ul. V. Pika. 4, Moscow, 129226, Russia

Abstract: Initial-boundary value problems for self-adjoint parabolic equations on a semiaxis and a semibounded strip are considered. For finite-difference $\sigma$-schemes, an alternative method for stating approximate transparent boundary conditions is suggested and conditions ensuring unconditional stability in the energy norm with respect to the initial data and free terms for a weight $\sigma\ge1/2$ are presented. The validity of these stability conditions in the case of discrete transparent boundary conditions is proved (by several methods), and the derivation of the latter conditions is revisited.

Key words: stability, finite-difference $\sigma$-scheme, approximate and discrete transparent boundary conditions, parabolic equations, unbounded domains.

UDC: 519.633

Received: 20.04.2006
Revised: 08.11.2006

 English version: Computational Mathematics and Mathematical Physics, 2007, 47:4, 644–663

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