Stability of a class of matrices with applications to absorbing boundary conditions for Schrödinger-type equations.
type: Item
instance of: scholarly article
title: Stability of a class of matrices with applications to absorbing boundary conditions for Schrödinger-type equations.
zbMATH Open document ID: 1067.65098
DOI: 10.1016/S0893-9659(04)90034-1
published in: Applied Mathematics Letters
publication date: 2005-02-25T00:00:00Z
review text: A class of tridiagonal complex matrices \(M_{N+1}(h)\) is investigated. The structure of these matrices is such that the coefficients depend on some positive parameter \(h>0\) and \(N=L/h\) for some positive constant \(L\). First, the stability of a class of matrices without the dependence on \(h\) under some conditions on the coefficients is proved. Then also for the original type of matrices under some conditions on the coefficients is proved that all the eigenvalues have negative real part. Practical applications of this theoretical result presented for numerical solving a Schrödinger type partial differential equation with local absorbing boundary condition of order ABC(1,1) that are developed in a previous paper of the author [ibid. 17, No.~2, 181--188 (2004; reviewed above)]. The numerical problem is derived by using a discretization by finite differences and also a spatial discretization for the boundary condition ABC(1,1) is derived. Than the stability for the matrix of this practical problem, using previous results presented before, is proved.
reviewed by: Angela Handlovičová
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35Q40
zbMATH DE Number: 2138573
zbMATH Keywords: absorbing boundary conditions
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: semidiscretization
zbMATH Keywords: stability
author: Nuria Reguera
MaRDI profile type: Publication
cites work: Weak Ill-Posedness of Spatial Discretizations of Absorbing Boundary Conditions for Schrödinger-Type Equations
cites work: Discrete Absorbing Boundary Conditions for Schrödinger-Type Equations. Construction and Error Analysis
cites work: Transparent and absorbing boundary conditions for the schrödinger equation in a bounded domain
cites work: Absorbing Boundary Conditions for the Schrödinger Equation
cites work: Absorbing Boundary Conditions for the Discretization Schemes of the One-Dimensional Wave Equation
full work available at URL: s0893-9659(04)90034-1
OpenAlex ID: W2075650408
description: scientific article; zbMATH DE number 2138573