Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems

Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems
Author :
Publisher : Springer Science & Business Media
Total Pages : 482
Release :
ISBN-10 : 9781461212089
ISBN-13 : 1461212081
Rating : 4/5 (081 Downloads)

Book Synopsis Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems by : Eusebius Doedel

Download or read book Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems written by Eusebius Doedel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating more complicated objects, such as higher- codimension bifurcations of fixed points, periodic orbits, and connecting orbits, as well as the calcuation of invariant manifolds. Another challenge is to extend the applicability of algorithms to the very large systems that result from discretizing partial differential equations. Even the calculation of steady states and their linear stability can be prohibitively expensive for large systems (e.g. 10_3- -10_6 equations) if attempted by simple direct methods. Several of the papers in this volume treat computational methods for low and high dimensional systems and, in some cases, their incorporation into software packages. A few papers treat fundamental theoretical problems, including smooth factorization of matrices, self -organized criticality, and unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics, and mechanical engineering.


Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems Related Books

Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems
Language: en
Pages: 482
Authors: Eusebius Doedel
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

GET EBOOK

The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory a
Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems
Language: en
Pages: 498
Authors: Eusebius Doedel
Categories:
Type: BOOK - Published: 2000-03-17 - Publisher:

GET EBOOK

Numerical Continuation Methods for Dynamical Systems
Language: en
Pages: 411
Authors: Bernd Krauskopf
Categories: Science
Type: BOOK - Published: 2007-11-06 - Publisher: Springer

GET EBOOK

Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theor
Numerical Methods for Bifurcations of Dynamical Equilibria
Language: en
Pages: 384
Authors: Willy J. F. Govaerts
Categories: Mathematics
Type: BOOK - Published: 2000-01-01 - Publisher: SIAM

GET EBOOK

Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and con
Numerical Continuation Methods
Language: en
Pages: 402
Authors: Eugene L. Allgower
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

GET EBOOK

Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. T