Construction of the solutions of difference equations in the field of Mikusiński operators
type: Item
instance of: scholarly article
title: Construction of the solutions of difference equations in the field of Mikusiński operators
zbMATH Open document ID: 0908.44003
author: Djurdjica Takači
author: Arpad Takači
published in: Rocky Mountain Journal of Mathematics
publication date: 1998-10-06T00:00:00Z
full work available at URL: CONT27-4.html
review text: The difference equation (i) \(a_nu_{n-1}+ b_nu_n+ c_nu_{n+1}= f_n\), \(n= 1,\dots, N-1\), is solved for given boundary values \(u_0\), \(u_N\) in the following case: The coefficients are continuous operator functions, and the boundary values are operators, both in the field of Mikusiński. The authors discuss, whether the solutions are continuous functions, or at least continuous operator functions, or not. In the case that (i) is the discretization of a differential equation, the error between the solutions is estimated.
Mathematics Subject Classification ID: 44A40
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 1206699
zbMATH Keywords: difference equations
zbMATH Keywords: Mikusiński operational calculus
zbMATH Keywords: error bound
zbMATH Keywords: discretization
reviewed by: Lothar Berg
MaRDI profile type: Publication
OpenAlex ID: W1967121857
cites work: Q3785375
cites work: Q4325607
cites work: Q4288786
cites work: Q4764732
cites work: An algorithm for the approximate solution of operator difference equations
DOI: 10.1216/RMJM/1181071873
description: scientific article; zbMATH DE number 1206699