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ABSTRACT
Difference equations are at the root of many numerical analysis algorithms and are equally pervasive in combinatorics. This article opens with a few definitions and examples, followed by a discussion of scalar linear difference equations and non-constant coefficient equations. Singular linear difference systems are then examined in depth. One of the ways they are approached is through firstly analyzing reductions of difference systems, the reducibility of invertible difference linear systems, the order of a difference linear system, etc.
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Read the articleAUTHORS
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Guoting CHEN: Senior Lecturer, Paul-Painlevé Laboratory, CNRS - UFR of Mathematics, University of Lille-1
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Jean DELLA DORA: Professor, Jean-Kuntzmann Laboratory, CNRS - Institut national polytechnique de Grenoble (INPG), Joseph-Fourier University
INTRODUCTION
Difference equations have been the basis of applied analysis since L. Euler, P. L. Tchebycheff and A. A. Markov. Today, they are the basis of many numerical analysis algorithms and are ubiquitous in combinatorics.
But can we talk about a theory of difference equations?
The answer is certainly no. Non-linear difference equations remain a difficult and topical subject for mathematicians (as do ordinary differential equations; see the articles "Linear differential equations"
However, one part of the theory is well understood: the part relating to linear difference equations. In this presentation, we shall confine ourselves to the fundamental points.
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