Perturbation methods, bifurcation theory and computer algebra
type: Item
instance of: scholarly article
title: Perturbation methods, bifurcation theory and computer algebra
zbMATH Open document ID: 0651.34001
author: Dieter Armbruster
author: Richard Rand
published in: Applied Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
review text: The book under review is not a usual one. As stated clearly in the preface the purpose of the authors was ``to provide computer algebra programs which implement a number of popular perturbation methods''. They do this with great success, and the result is a fine textbook, that must be worked and not only read. The background necessary to read the book is quite elementary, one needs only some background in differential equations and familiarity with computers. The computer algebra system used in the book is MACSYMA, and an appendix is provided to guide the reader, but one needs more. The material is presented in the form of worked examples and the reader is supposed to do a lot of work to understand really what is going on. Computer programs are provided to guide the numerical experiments. Besides the perturbation methods presented there is a lot of information about elementary bifurcations: folds, pitchforks, Hoff, both ordinary and partial differential equations are discussed. Each chapter of the book describes a differential perturbation method: Lindstedt, Center manifold, Normal forms, Two variable expansion method, Averaging, Lie transforms, Lyapunov-Schmidt reduction. Each method is nicely discussed, through very good examples. The methods are compared. Limitation and advantages of each are clearly pointed out in form of examples. Finally, it is a pleasure to ``work'' the book.
Mathematics Subject Classification ID: 34-01
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 35B20
zbMATH DE Number: 4061656
zbMATH Keywords: computer algebra programs
zbMATH Keywords: perturbation methods
zbMATH Keywords: bifurcations
zbMATH Keywords: folds
zbMATH Keywords: pitchforks
zbMATH Keywords: Hoff
zbMATH Keywords: examples
describes a project that uses: MACSYMA
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4061656