On modification of Samoilenko's numerical-analytic method of solving boundary value problems for difference equations
type: Item
instance of: scholarly article
title: On modification of Samoilenko's numerical-analytic method of solving boundary value problems for difference equations
zbMATH Open document ID: 0786.65116
author: Marian Kwapisz
published in: Applications of Mathematics
publication date: 1993-10-13T00:00:00Z
full work available at URL: https://eudml.org/doc/15741
review text: The author studies some modification of Samoilenko's numerical analytic method in relation to the difference boundary value problem \(x(n) = f(x(n))\), \(n\in \{0,1,\dots,m-1\}\), \(Cx(0) + Dx(m) = d\), in any linear space equipped with a \(k\)-dimensional vector norm. He presents conditions which allow to state when the auxiliary equation \[ x(n) = x_ 0 + \sum^{n-1}_{i=0}f(x(i)) + \omega(n)[\varphi(x_ 0) + \sum^{m- 1}_{i=0}f(x(i))],\quad n\in\{0,1,\dots,m-1\} \] possesses a unique solution and this solution can be obtained by the method of successive approximations. Some generalizations are presented.
Mathematics Subject Classification ID: 65Q05
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 428198
zbMATH Keywords: boundary value problems
zbMATH Keywords: difference equations
zbMATH Keywords: method of successive approximations
reviewed by: Jerzy Ryszard Popenda
MaRDI profile type: Publication
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OpenAlex ID: W2287554636
DOI: 10.21136/AM.1993.104540
description: scientific article; zbMATH DE number 428198