Computational Methods For Nonlinear Dynamical Systems
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Computational Methods For Nonlinear Dynamical Systems
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Author : Xuechuan Wang
language : en
Publisher: Elsevier
Release Date : 2022-09-28
Computational Methods For Nonlinear Dynamical Systems written by Xuechuan Wang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-28 with Technology & Engineering categories.
Computational Methods for Nonlinear Dynamical Systems: Theory and Applications in Aerospace Engineering proposes novel ideas and develops highly-efficient and accurate methods for solving nonlinear dynamic systems, drawing inspiration from the weighted residual method and the asymptotic method. Proposed methods can be used both for real-time simulation and the analysis of nonlinear dynamics in aerospace engineering. The book introduces global estimation methods and local computational methods for nonlinear dynamic systems. Starting from the classic asymptotic, finite difference and weighted residual methods, typical methods for solving nonlinear dynamic systems are considered. In addition, new high-performance methods are proposed, such as time-domain collocation and local variational iteration. The book summarizes and develops computational methods for strongly nonlinear dynamic systems and considers the practical application of the methods within aerospace engineering. - Presents global methods for solving periodic nonlinear dynamical behaviors - Gives local methods for solving transient nonlinear responses - Outlines computational methods for linear, nonlinear, ordinary and partial differential equations - Emphasizes the development of accurate and efficient numerical methods that can be used in real-world missions - Reveals practical applications of methods through orbital mechanics and structural dynamics
Applied Nonlinear Dynamics
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Author : Ali H. Nayfeh
language : en
Publisher: John Wiley & Sons
Release Date : 2008-11-20
Applied Nonlinear Dynamics written by Ali H. Nayfeh 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 2008-11-20 with Science categories.
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
Nonlinear Dynamics In Computational Neuroscience
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Author : Fernando Corinto
language : en
Publisher: Springer
Release Date : 2018-06-19
Nonlinear Dynamics In Computational Neuroscience written by Fernando Corinto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-19 with Technology & Engineering categories.
This book provides an essential overview of computational neuroscience. It addresses a broad range of aspects, from physiology to nonlinear dynamical approaches to understanding neural computation, and from the simulation of brain circuits to the development of engineering devices and platforms for neuromorphic computation. Written by leading experts in such diverse fields as neuroscience, physics, psychology, neural engineering, cognitive science and applied mathematics, the book reflects the remarkable advances that have been made in the field of computational neuroscience, an emerging discipline devoted to the study of brain functions in terms of the information-processing properties of the structures forming the nervous system. The contents build on the workshop “Nonlinear Dynamics in Computational Neuroscience: from Physics and Biology to ICT,” which was held in Torino, Italy in September 2015.
Numerical Methods For Nonlinear Engineering Models
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Author : John R. Hauser
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-24
Numerical Methods For Nonlinear Engineering Models written by John R. Hauser 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 2009-03-24 with Technology & Engineering categories.
There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.
Numerical Methods For Nonlinear Variational Problems
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Author : Roland Glowinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Numerical Methods For Nonlinear Variational Problems written by Roland Glowinski 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 2013-06-29 with Science categories.
Many mechanics and physics problems have variational formulations making them appropriate for numerical treatment by finite element techniques and efficient iterative methods. This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids. Finite element approximations and non-linear relaxation, augmented Lagrangians, and nonlinear least square methods are all covered in detail, as are many applications. "Numerical Methods for Nonlinear Variational Problems", originally published in the Springer Series in Computational Physics, is a classic in applied mathematics and computational physics and engineering. This long-awaited softcover re-edition is still a valuable resource for practitioners in industry and physics and for advanced students.
Numerical Methods For Unconstrained Optimization And Nonlinear Equations
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Author : J. E. Dennis, Jr.
language : en
Publisher: SIAM
Release Date : 1996-12-01
Numerical Methods For Unconstrained Optimization And Nonlinear Equations written by J. E. Dennis, Jr. and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-01 with Mathematics categories.
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Computational Methods In Stochastic Dynamics
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Author : Manolis Papadrakakis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-03
Computational Methods In Stochastic Dynamics written by Manolis Papadrakakis 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 2012-10-03 with Technology & Engineering categories.
The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification and its influence on the reliability of the computational models are continuously gaining in significance. In particular, the problems of dynamic response analysis and reliability assessment of structures with uncertain system and excitation parameters have been the subject of continuous research over the last two decades as a result of the increasing availability of powerful computing resources and technology. This book is a follow up of a previous book with the same subject (ISBN 978-90-481-9986-0) and focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The selected chapters are authored by some of the most active scholars in their respective areas and represent some of the most recent developments in this field. The book consists of 21 chapters which can be grouped into several thematic topics including dynamic analysis of stochastic systems, reliability-based design, structural control and health monitoring, model updating, system identification, wave propagation in random media, seismic fragility analysis and damage assessment. This edited book is primarily intended for researchers and post-graduate students who are familiar with the fundamentals and wish to study or to advance the state of the art on a particular topic in the field of computational stochastic structural dynamics. Nevertheless, practicing engineers could benefit as well from it as most code provisions tend to incorporate probabilistic concepts in the analysis and design of structures.
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.
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.
Structural Dynamic Systems Computational Techniques And Optimization
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Author : Cornelius T. Leondes
language : en
Publisher: CRC Press
Release Date : 1999-03-22
Structural Dynamic Systems Computational Techniques And Optimization written by Cornelius T. Leondes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-22 with Mathematics categories.
Computational techniques for the analysis and design of structural dynamic systems using numerical methods have been the focus of an enormous amount of research for several decades. In general, the numerical methods utilized to solve these problems include two phases: (a) spatial discretization by either the finite element method (FEM) or the finite difference method (FDM), and (b) solution of systems of time dependent second-order ordinary differential equations. In addition, the significantly powerful advances in computer systems capabilities have put on the desks of structural systems designers enormous computing power either by means of increasingly effective computer workstations or else through PCs (personal computers), whose increasing power has succeeded in marginalizing the computational power differences between PCs and workstations in many cases. This volume is a comprehensive treatment of the issues involved in computational techniques in structural dynamic systems.