Monotone-iterative method for solving antiperiodic nonlinear boundary value problems for generalized delay difference equations with maxima
type: Item
instance of: scholarly article
title: Monotone-iterative method for solving antiperiodic nonlinear boundary value problems for generalized delay difference equations with maxima
zbMATH Open document ID: 1291.39001
DOI: 10.1155/2013/571954
author: Angel Golev
author: Snezhana Hristova
author: S. I. Nenov
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: A nonlinear generalized difference equation with both delays and the maximum value of the unknown function over a discrete past time interval are studied. A nonlinear boundary value problem of antiperiodic type for the given difference equation is set up. One of the main characteristics of the considered difference equation is the presence of the unknown function in both sides of the equation. It leads to impossibility for using the step method for explicit solving of the nonlinear difference equation. In this paper, an approximate method, namely, the monotone iterative technique, is applied to solve the problem. An important feature of the given algorithm is that each successive approximation of the unknown solution is equal to the unique solution of an appropriately constructed initial value problem for a linear difference equation with ``maxima,'' and an algorithm for its explicit solving is given. Also, each approximation is a lower/upper solution of the given nonlinear boundary value problem. The suggested scheme for approximate solving is computer realized, and it is applied to a particular example, which is a generalization of a model in population dynamics.
Mathematics Subject Classification ID: 39A05
Mathematics Subject Classification ID: 39A22
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 39A60
zbMATH DE Number: 6307009
Wikidata QID: Q58917141
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/571954
OpenAlex ID: W1986979490
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description: scientific article; zbMATH DE number 6307009