Stability of nonlocal difference schemes in a subspace
type: Item
instance of: scholarly article
title: Stability of nonlocal difference schemes in a subspace
zbMATH Open document ID: 1261.65091
DOI: 10.1134/S0012266112070051
author: A. V. Gulin
published in: Differential Equations
publication date: 2012-11-14T00:00:00Z
review text: The author considers a family of two-layer difference schemes for the heat equation with nonlocal boundary conditions containing a parameter \(\gamma\). In some interval \(\gamma \in (1, \gamma_+)\), the spectrum of the main difference operator contains a unique eigenvalue \(\lambda_0\) in the left complex half-plane, while the remaining eigenvalues \(\lambda_1, \lambda_2, \ldots , \lambda_{N-1}\) lie in the right half-plane. The author represents the corresponding grid space \(H_N\) as the direct sum \(H_N = H_0\oplus H_{N-1}\) of a one-dimensional subspace and the subspace \(H_{N-1}\) that is the linear span of eigenvectors \(\mu^{(1)}, \mu^{(2)}, \dots, \mu^{(N-1)}\). The author introduces the notion of stability in the subspace \(H_{N-1}\) and derive a stability criterion.
reviewed by: Yasar Sozen
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 6105643
zbMATH Keywords: stability
zbMATH Keywords: two-layer difference schemes
zbMATH Keywords: heat equation
zbMATH Keywords: nonlocal boundary conditions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6105643