Difference equations in Banach spaces

Agarwal, RP, Thompson, HB and Tisdell, CC (2003) Difference equations in Banach spaces. Computers & Mathematics With Applications, 45 6-9: 1437-1444. doi:10.1016/S0898-1221(03)00100-7

Author Agarwal, RP
Thompson, HB
Tisdell, CC
Title Difference equations in Banach spaces
Journal name Computers & Mathematics With Applications   Check publisher's open access policy
ISSN 0898-1221; 0898-1211
Publication date 2003
Sub-type Article (original research)
DOI 10.1016/S0898-1221(03)00100-7
Volume 45
Issue 6-9
Start page 1437
End page 1444
Total pages 8
Editor E.Y. Rodin
Place of publication United Kingdom
Publisher Pergamon
Collection year 2003
Language eng
Subject C1
230107 Differential, Difference and Integral Equations
780101 Mathematical sciences
Abstract Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.
Keyword Computer Science, Interdisciplinary Applications
Mathematics, Applied
Two Point Boundary Value Problem
Difference Equations
Second-order Ordinary Differential Equations
A Priori Bounds
Existence Of Solutions
Discrete Equations
Q-Index Code C1

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Created: Tue, 14 Aug 2007, 19:14:41 EST