Theory of difference equations: Numerical methods and applications
type: Item
instance of: scholarly article
title: Theory of difference equations: Numerical methods and applications
zbMATH Open document ID: 0683.39001
published in: Mathematics in Science and Engineering
publication date: 1992-09-17T00:00:00Z
review text: The book consists of seven chapters and three appendices. The first chapter presents some necessary preliminaries. The second chapter is devoted to the presentation of such important methods as variation of constants and generating functions for finding a solution of a linear difference equation. Here the authors also consider the stability and absolute stability of solutions. Chapter three deals with linear systems of difference equations and an extension of previously described methods for one difference equation to the case of a system. Chapter four presents some more deep issues of stability theory such as linear equations with periodic coefficients, use of the comparison principle, Lyapunov functions, domain of asymptotic stability, total and practical stabilities. Chapter five deals with applications of the previously presented results to numerical analysis, iterative methods, Miller's, Olver's, Clenshaw's algorithms, and monotone iterative methods. Chapter six presents some numerical methods for differential equations and their connections with the corresponding methods for difference equations. Chapter seven deals with some applications of the previous results to such models of real world phenomena as population dynamics, distillation of a binary liquid, economics, traffic in channels, etc. The appendices present useful facts on algebra and calculus of matrices, Schur criterium, Chebyshev polynomials. All the chapters contain problems which help a lot the reader to understand the main part of the text.
Mathematics Subject Classification ID: 39Axx
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 39-02
Mathematics Subject Classification ID: 65Q05
Mathematics Subject Classification ID: 65N22
zbMATH DE Number: 40972
zbMATH Keywords: Miller's algorithm
zbMATH Keywords: Olver's algorithm
zbMATH Keywords: textbook
zbMATH Keywords: variation of constants
zbMATH Keywords: generating functions
zbMATH Keywords: linear difference equation
zbMATH Keywords: absolute stability
zbMATH Keywords: linear systems
zbMATH Keywords: periodic coefficients
zbMATH Keywords: comparison principle
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: asymptotic stability
zbMATH Keywords: Clenshaw's algorithms
zbMATH Keywords: monotone iterative methods
zbMATH Keywords: population dynamics
zbMATH Keywords: economics
zbMATH Keywords: traffic in channels
author: V. Lakshmikantham
author: Donato Trigiante
reviewed by: Yu. V. Kostarchuk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 40972