 Approximative solutions to difference equations of neutral typeJanusz Migda Applied Mathematics and Computation, 2015, vol. 268, issue C, 763-774 Abstract: Asymptotic properties of solutions to difference equations of the form Δm(xn−unxn−k)=anf(xn)+bnare studied. Replacing the sequence u by its limit and the right side of the equation by zero we obtain an equation which we call the fundamental equation. First we investigate the space of all solutions of the fundamental equation. We show that any such solution is a sum of a polynomial sequence and a product of a geometric sequence and a periodic sequence. Next, using a new version of the Krasnoselski fixed point theorem and the iterated remainder operator, we establish sufficient conditions under which a given solution of the fundamental equation is an approximative solution to the above equation. Our approach, based on the iterated remainder operator, allows us to control the degree of approximation. In this paper we use o(ns), for a given nonpositive real s, as a measure of approximation. Keywords: Neutral difference equation; Approximative solution; Prescribed asymptotic behavior; Iterated remainder operator; Regional topology; Krasnoselski fixed point theorem (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:763-774 DOI: 10.1016/j.amc.2015.06.097 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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