Continuation Techniques and Bifurcation Problems
Published on 1. January 1990
Book
Paperback/Softback
V, 218 pages
978-3-7643-2397-4 (ISBN)
Description
The analysis of parameter-dependent nonlinear has received much attention in recent years. Numerical continuation techniques allow the efficient computation of solution branches in a one-parameter problem. In many cases continuation procedures are used as part of a more complete analysis of a nonlinear problem, based on bifurcation theory and singularity theory. These theories contribute to the understanding of many nonlinear phenomena in nature and they form the basis for various analytical and numerical tools, which provide qualitative and quantitative results about nonlinear systems. In this issue we have collected a number of papers dealing with continuation techniques and bifurcation problems. Readers familiar with the notions of continuation and bifurcation will find recent research results addressing a variety of aspects in this issue. Those who intend to learn about the field or a specific topic in it may find it useful to first consult earlier literature on the numerical treatment of these problems together with some theoretical background. The papers in this issue fall naturally into different groups.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1990
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
10 s/w Abbildungen
V, 218 p. 10 illus.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 13 mm
Weight
402 gr
ISBN-13
978-3-7643-2397-4 (9783764323974)
DOI
10.1007/978-3-0348-5681-2
Schweitzer Classification
Content
Large sparse continuation problems.- Continuation for parametrized nonlinear variational inequalities.- A multi-grid continuation strategy for parameter-dependent variational inequalities.- Continuation methods in semiconductor device simulation.- Stepsize selection in continuation procedures and damped Newton's method.- Symmetry breaking and semilinear elliptic equations.- Computational methods for bifurcation problems with symmetries-with special attention to steady state and Hopf bifurcation points.- A note on the calculation of paths of Hopf bifurcations.- Computation of cusp singularities for operator equations and their discretizations.- Numerical computation of heteroclinic orbits.- Interaction between fold and Hopf curves leads to new bifurcation phenomena.- Bi-periodicity in an isothermal autocatalytic reaction-diffusion system.- Generic one-parameter bifurcations in the motion of a simple robot.