Difference inequalities generated by impulsive parabolic differential-functional problems
type: Item
instance of: scholarly article
title: Difference inequalities generated by impulsive parabolic differential-functional problems
zbMATH Open document ID: 0895.65039
DOI: 10.1016/S0377-0427(97)00123-4
author: Katarzyna Pączkowska-Prządka
published in: Journal of Computational and Applied Mathematics
publication date: 1998-09-02T00:00:00Z
review text: An abstract parabolic differential-functional initial-boundary value problem with impulses is considered. Together with this problem, the author formulates a corresponding finite difference problem. The finite difference equations are of explicit type. The main goal of this paper is the convergence theorem for a given finite difference approximation of the original problem. The proof of the convergence is based on certain monotonicity property of the finite difference approximation considered here. This property is expressed in the form of some finite difference recurrent inequality (see for example Theorem 1). Under a number of hypotheses concerning the original problem and its finite difference approximation (including stability of the approximate problem) the author proves her convergence result. In fact, this kind of finite difference approximation could be only conditionally stable. This problem is not discussed here -- the author simply assumes stability. The special section of the paper is devoted to the almost linear problem. One numerical example is given.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 1084112
zbMATH Keywords: difference inequalities
zbMATH Keywords: convergence
zbMATH Keywords: finite difference
zbMATH Keywords: stability
zbMATH Keywords: numerical example
zbMATH Keywords: abstract parabolic differential-functional initial-boundary value problem with impulses
reviewed by: Krzysztof Moszyński
MaRDI profile type: Publication
cites work: On first order impulsive partial differential inequalities
cites work: Difference methods for impulsive differential-functional equations
cites work: Q4871975
cites work: Q3995625
cites work: Q4003924
cites work: Q4277641
cites work: Impulsive nonlocal nonlinear parabolic differential problems
cites work: Q4321711
cites work: Q3363749
cites work: A difference method for certain hyperbolic systems of non-linear partial differential equations of the first order
cites work: Q4190086
cites work: Q3041583
cites work: Q3222664
cites work: On difference inequalities corresponding to partial differential inequalities of the first order
cites work: Difference Methods for Non-Linear Partial Differential-Functional Equations of the First Order
cites work: Q4008417
description: scientific article; zbMATH DE number 1084112