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Dynamical Systems and Numerical Analysis

1998-11-28 Mathematics
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Release : 1998-11-28
Genre : Mathematics
Kind : eBook
Book Rating : 638/5 ( reviews)

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Book Synopsis Dynamical Systems and Numerical Analysis by : Andrew Stuart

Download or read book Dynamical Systems and Numerical Analysis written by Andrew Stuart. This book was released on 1998-11-28. Available in PDF, EPUB and Kindle. Book excerpt: The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.

Numerical Methods for Nonsmooth Dynamical Systems

2008-01-30 Technology & Engineering
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Release : 2008-01-30
Genre : Technology & Engineering
Kind : eBook
Book Rating : 923/5 ( reviews)

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Book Synopsis Numerical Methods for Nonsmooth Dynamical Systems by : Vincent Acary

Download or read book Numerical Methods for Nonsmooth Dynamical Systems written by Vincent Acary. This book was released on 2008-01-30. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.

Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 081/5 ( reviews)

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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. This book was released on 2012-12-06. 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 Continuation Methods for Dynamical Systems

2007-11-06 Science
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Release : 2007-11-06
Genre : Science
Kind : eBook
Book Rating : 563/5 ( reviews)

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Book Synopsis Numerical Continuation Methods for Dynamical Systems by : Bernd Krauskopf

Download or read book Numerical Continuation Methods for Dynamical Systems written by Bernd Krauskopf. This book was released on 2007-11-06. Available in PDF, EPUB and Kindle. Book excerpt: Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

Numerical Methods for Bifurcations of Dynamical Equilibria

2000-01-01 Mathematics
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Release : 2000-01-01
Genre : Mathematics
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Book Rating : 543/5 ( reviews)

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Book Synopsis Numerical Methods for Bifurcations of Dynamical Equilibria by : Willy J. F. Govaerts

Download or read book Numerical Methods for Bifurcations of Dynamical Equilibria written by Willy J. F. Govaerts. This book was released on 2000-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.

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