Implicit difference schemes for evolution functional differential equations
type: Item
instance of: scholarly article
title: Implicit difference schemes for evolution functional differential equations
zbMATH Open document ID: 1215.35163
DOI: 10.4171/ZAA/1427
author: Z. Kamont
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2011-03-07T00:00:00Z
review text: This paper deals with implicit difference schemes for quasilinear functional differential equations or systems. The paper is divided into two parts. In the first part, a new method of investigation of implicit difference schemes corresponding to initial boundary value problems for quasilinear evolution functional differential equations or systems is proposed. A general implicit difference functional problem with an unknown function of several variables is formulated. Sufficient conditions for the existence and uniqueness of a solution of the initial boundary value problem are given and some error estimates of approximate solutions are established. In the second part, the general results obtained before are applied to quasilinear functional systems with first order partial derivatives and to quasilinear parabolic problems.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 5862060
zbMATH Keywords: functional differential equations
zbMATH Keywords: stability and convergence
zbMATH Keywords: interpolating operators
zbMATH Keywords: implicit difference schemes
MaRDI profile type: Publication
cites work: Existence, uniqueness and continuous dependence for a hereditary nonlinear functional partial differential equation of the first order
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cites work: Implicit difference methods for parabolic functional differential equations
description: scientific article; zbMATH DE number 5862060