Dynamical Systems And Numerical Analysis
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Dynamical Systems And Numerical Analysis
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Author : Andrew Stuart
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-28
Dynamical Systems And Numerical Analysis written by Andrew Stuart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-28 with Mathematics categories.
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.
Dynamical Systems And Numerical Analysis
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Author : Andrew Stuart
language : en
Publisher: Cambridge University Press
Release Date : 1996-08-13
Dynamical Systems And Numerical Analysis written by Andrew Stuart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-13 with Mathematics categories.
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.
Dynamical Systems Method And Applications
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Author : Alexander G. Ramm
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-07
Dynamical Systems Method And Applications written by Alexander G. Ramm and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-07 with Mathematics categories.
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.
Numerical Methods For Nonsmooth Dynamical Systems
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Author : Vincent Acary
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-30
Numerical Methods For Nonsmooth Dynamical Systems written by Vincent Acary and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-30 with Technology & Engineering categories.
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.
Stochastic Dynamical Systems
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Author : J. Honerkamp
language : en
Publisher: Wiley-VCH
Release Date : 1993-12-31
Stochastic Dynamical Systems written by J. Honerkamp and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-31 with Stochastic processes categories.
Stochastic Dynamical Systems
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Author : Josef Honerkamp
language : en
Publisher: John Wiley & Sons
Release Date : 1996-12-17
Stochastic Dynamical Systems written by Josef Honerkamp and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-17 with Mathematics categories.
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.
Modelling And Control Of Dynamical Systems Numerical Implementation In A Behavioral Framework
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Author : Ricardo Zavala Yoe
language : en
Publisher: Springer
Release Date : 2008-06-24
Modelling And Control Of Dynamical Systems Numerical Implementation In A Behavioral Framework written by Ricardo Zavala Yoe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-24 with Computers categories.
The Behavioral Approach for systems and control deals directly with the solution of the differential equations which represent the system. This book reviews this approach and offers new theoretic results. The programs and algorithms are MATLAB based.
Numerical Methods For Bifurcations Of Dynamical Equilibria
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Author : Willy J. F. Govaerts
language : en
Publisher: SIAM
Release Date : 2000-01-01
Numerical Methods For Bifurcations Of Dynamical Equilibria written by Willy J. F. Govaerts and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
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.
Numerical Continuation Methods For Dynamical Systems
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Author : Bernd Krauskopf
language : en
Publisher: Springer
Release Date : 2007-11-06
Numerical Continuation Methods For Dynamical Systems written by Bernd Krauskopf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-06 with Science categories.
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.
Differential Equations
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Author : Marcelo Viana
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-07
Differential Equations written by Marcelo Viana and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-07 with Mathematics categories.
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time—pure and applied alike—ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques. The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman–Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincaré–Hopf index theorem. The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.