An effective numerical technique for solving a special class of ordinary difference equations
type: Item
instance of: scholarly article
title: An effective numerical technique for solving a special class of ordinary difference equations
zbMATH Open document ID: 0838.65128
DOI: 10.1016/0168-9274(95)00081-5
author: V. S. Ryaben'kij
author: S. V. Tsynkov
published in: Applied Numerical Mathematics
publication date: 1996-06-03T00:00:00Z
review text: The authors consider a system of ordinary difference equations of the form \[ Av_{m + 1} + Bv_m = f_{m + 1/2}, \quad m \in \mathbb{Z}. \tag{1} \] Here, \(A\) and \(B\) are square matrices with constant entries, and the right hand side is compactly supported, which means that the equation is homogeneous outside some finite mesh interval. Moreover, it is first assumed that the matrices \(Q = A^{-1} B\) and \(Q^{-1}\) exist, and that each eigenvalue \(\mu\) of \(Q\) satisfies \(|\mu |\neq 1\). Under the additional assumption that \(v_m \to 0\) for \(m \to \pm \infty\), it is shown that there is a unique solution of (1). Then the authors develop a numerical algorithm for the computation of this solution, and give a detailed discussion of the numerical stability and efficiency of their method. A discussion of the case where eigenvalues of \(Q\) of absolute value 1 exist, and some considerations on practical applications of the problem under consideration conclude the paper.
Mathematics Subject Classification ID: 65Q05
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 826020
zbMATH Keywords: system of ordinary difference equations
zbMATH Keywords: algorithm
zbMATH Keywords: numerical stability
reviewed by: Guido Walz
MaRDI profile type: Publication
full work available at URL: 0168-9274(95)00081-5
OpenAlex ID: W2050682580
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description: scientific article; zbMATH DE number 826020