Genre : Mathematics
Publisher : Cambridge University Press
ISBN_10 : 0521645638
Copyright Year : 1998-11-28
File Format : All Formats
File Download : 685
Price : FREE


E-BOOK EXCERPT

This book unites the study of dynamical systems and numerical solution of differential equations. 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 formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release

Genre : Mathematics
Publisher : Cambridge University Press
ISBN_10 : 0521496721
Copyright Year : 1996-08-13
File Format : All Formats
File Download : 710
Price : FREE


E-BOOK EXCERPT

This book unites the study of dynamical systems and numerical solution of differential equations. 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 formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release

Genre : Technology & Engineering
Publisher : Springer Science & Business Media
ISBN_10 : 3540753923
Copyright Year : 2008-01-30
File Format : All Formats
File Download : 525
Price : FREE


E-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.

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release

Genre : Mathematics
Publisher : John Wiley & Sons
ISBN_10 : 0471188344
Copyright Year : 1993-11-12
File Format : All Formats
File Download : 552
Price : FREE


E-BOOK EXCERPT

This unique volume introduces the reader to the mathematical language for complex systems and is ideal for students who are starting out in the study of stochastical dynamical systems. Unlike other books in the field it covers a broad array of stochastic and statistical methods.

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release

Genre :
Publisher :
ISBN_10 : STANFORD:36105046337346
Copyright Year : 1993
File Format : All Formats
File Download : 234
Price : FREE


E-BOOK EXCERPT

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release

Genre : Mathematics
Publisher : Springer Science & Business Media
ISBN_10 : 9781461212089
Copyright Year : 2012-12-06
File Format : All Formats
File Download : 481
Price : FREE


E-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.

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release

Genre :
Publisher :
ISBN_10 : CORNELL:31924077495384
Copyright Year : 1996
File Format : All Formats
File Download : 514
Price : FREE


E-BOOK EXCERPT

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release

Genre : Bifurcation theory
Publisher : SIAM
ISBN_10 : 0898719542
Copyright Year : 2000-01-01
File Format : All Formats
File Download : 362
Price : FREE


E-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.

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release

Genre : Mathematics
Publisher : John Wiley & Sons
ISBN_10 : 9781118199602
Copyright Year : 2013-06-07
File Format : All Formats
File Download : 576
Price : FREE


E-BOOK EXCERPT

Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering. Additional featured topics include: General nonlinear operator equations Operators satisfying a spectral assumption Newton-type methods without inversion of the derivative Numerical problems arising in applications Stable numerical differentiation Stable solution to ill-conditioned linear algebraic systems Throughout the chapters, the authors employ the use of figures and tables to help readers grasp and apply new concepts. Numerical examples offer original theoretical results based on the solution of practical problems involving ill-conditioned linear algebraic systems, and stable differentiation of noisy data. Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellent book for courses on numerical analysis, dynamical systems, operator theory, and applied mathematics at the graduate level. The book also serves as a valuable resource for professionals in the fields of mathematics, physics, and engineering.

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release

Genre : Science
Publisher : Springer
ISBN_10 : 9781402063565
Copyright Year : 2007-11-06
File Format : All Formats
File Download : 399
Price : FREE


E-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.

#1Bestseller in [pdf] [tuebl] [kindle] [epub] [mobi] [audiobook], #1 e-Book New Release