Perturbation Methods, Bifurcation Theory and Computer Algebra

Softcover Nachdruck of the original 1. Auflage 1987
ISBN: 978-0-387-96589-5
Verlag: Springer

Buch, Englisch, Band 65, 251 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 400 g

Reihe: Applied Mathematical Sciences

Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.

Zielgruppe

Research

Autoren/Hrsg.

Armbruster, Dieter

Rand, Richard H.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

1 Lindstedt’s Method.- 2 Center Manifolds.- 3 Normal Forms.- 4 Two Variable Expansion Method.- 5 Averaging.- 6 Lie Transforms.- 7 Liapunov-Schmidt Reduction.- Appendix Introduction to MACSYMA.- References.