Introduction To Numerical Continuation Methods

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Introduction to Numerical Continuation Methods

Eugene L. Allgower,Kurt Georg
Introduction to Numerical Continuation Methods Book PDF

Author : Eugene L. Allgower,Kurt Georg
Publisher : SIAM
Page : 409 pages
File Size : 49,9 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9780898715446

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Introduction to Numerical Continuation Methods by Eugene L. Allgower,Kurt Georg Pdf

Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.

Numerical Continuation Methods

Eugene L. Allgower,Kurt Georg
Numerical Continuation Methods Book PDF

Author : Eugene L. Allgower,Kurt Georg
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642612572

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Numerical Continuation Methods by Eugene L. Allgower,Kurt Georg Pdf

Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.

Introduction to Numerical Continuation Methods

Eugene L. Allgower,Kurt Georg
Introduction to Numerical Continuation Methods Book PDF

Author : Eugene L. Allgower,Kurt Georg
Publisher : SIAM
Page : 413 pages
File Size : 45,7 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898719151

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Introduction to Numerical Continuation Methods by Eugene L. Allgower,Kurt Georg Pdf

Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. The book also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals. To help potential users of numerical continuation methods create programs adapted to their particular needs, this book presents pseudo-codes and Fortran codes as illustrations. Since it first appeared, many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds have been written. The original extensive bibliography has been updated in the SIAM Classics edition to include more recent references and several URLs so users can look for codes to suit their needs. Audience: this book continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business. A background in elementary analysis and linear algebra are adequate prerequisites for reading this book; some knowledge from a first course in numerical analysis may also be helpful.

Numerical Continuation Methods for Dynamical Systems

Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque
Numerical Continuation Methods for Dynamical Systems Book PDF

Author : Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque
Publisher : Springer
Page : 0 pages
File Size : 43,8 Mb
Release : 2014-10-30
Category : Science
ISBN : 9400797028

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Numerical Continuation Methods for Dynamical Systems by Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque Pdf

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 Continuation Methods for Dynamical Systems

Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque
Numerical Continuation Methods for Dynamical Systems Book PDF

Author : Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque
Publisher : Springer
Page : 399 pages
File Size : 48,6 Mb
Release : 2007-07-26
Category : Science
ISBN : 1402063555

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Numerical Continuation Methods for Dynamical Systems by Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque Pdf

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 Continuation and Bifurcation in Nonlinear PDEs

Hannes Uecker
Numerical Continuation and Bifurcation in Nonlinear PDEs Book PDF

Author : Hannes Uecker
Publisher : SIAM
Page : 380 pages
File Size : 48,8 Mb
Release : 2021-08-19
Category : Mathematics
ISBN : 9781611976618

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Numerical Continuation and Bifurcation in Nonlinear PDEs by Hannes Uecker Pdf

This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. After a concise review of some analytical background and numerical methods, the author explains the free MATLAB package pde2path by using a large variety of examples with demo codes that can be easily adapted to the reader's given problem. Numerical Continuation and Bifurcation in Nonlinear PDEs will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.

Numerical Methods for Bifurcations of Dynamical Equilibria

Willy J. F. Govaerts
Numerical Methods for Bifurcations of Dynamical Equilibria Book PDF

Author : Willy J. F. Govaerts
Publisher : SIAM
Page : 384 pages
File Size : 51,9 Mb
Release : 2000-01-01
Category : Mathematics
ISBN : 0898719542

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Numerical Methods for Bifurcations of Dynamical Equilibria by Willy J. F. Govaerts Pdf

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.

Introduction to Numerical Methods for Variational Problems

Hans Petter Langtangen,Kent-Andre Mardal
Introduction to Numerical Methods for Variational Problems Book PDF

Author : Hans Petter Langtangen,Kent-Andre Mardal
Publisher : Springer Nature
Page : 395 pages
File Size : 54,7 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9783030237882

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Introduction to Numerical Methods for Variational Problems by Hans Petter Langtangen,Kent-Andre Mardal Pdf

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Handbook of Dynamical Systems

B. Fiedler
Handbook of Dynamical Systems Book PDF

Author : B. Fiedler
Publisher : Gulf Professional Publishing
Page : 1099 pages
File Size : 48,5 Mb
Release : 2002-02-21
Category : Science
ISBN : 9780080532844

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Handbook of Dynamical Systems by B. Fiedler Pdf

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Solving Polynomial Equations

Alicia Dickenstein
Solving Polynomial Equations Book PDF

Author : Alicia Dickenstein
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 43,8 Mb
Release : 2005-04-27
Category : Computers
ISBN : 9783540243267

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Solving Polynomial Equations by Alicia Dickenstein Pdf

This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.

Singularities of Robot Mechanisms

Oriol Bohigas,Montserrat Manubens,Lluís Ros
Singularities of Robot Mechanisms Book PDF

Author : Oriol Bohigas,Montserrat Manubens,Lluís Ros
Publisher : Springer
Page : 184 pages
File Size : 54,6 Mb
Release : 2016-09-08
Category : Technology & Engineering
ISBN : 9783319329222

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Singularities of Robot Mechanisms by Oriol Bohigas,Montserrat Manubens,Lluís Ros Pdf

This book presents the singular configurations associated with a robot mechanism, together with robust methods for their computation, interpretation, and avoidance path planning. Having such methods is essential as singularities generally pose problems to the normal operation of a robot, but also determine the workspaces and motion impediments of its underlying mechanical structure. A distinctive feature of this volume is that the methods are applicable to nonredundant mechanisms of general architecture, defined by planar or spatial kinematic chains interconnected in an arbitrary way. Moreover, singularities are interpreted as silhouettes of the configuration space when seen from the input or output spaces. This leads to a powerful image that explains the consequences of traversing singular configurations, and all the rich information that can be extracted from them. The problems are solved by means of effective branch-and-prune and numerical continuation methods that are of independent interest in themselves. The theory can be put into practice as well: a companion web page gives open access to implementations of the algorithms and the corresponding input files. Using them, the reader can gain hands-on experience on the topic, or analyse new mechanisms beyond those examined in the text. Overall, the book contributes new tools for robot design, and constitutes a single reference source of knowledge that is otherwise dispersed in the literature.

Numerical Algorithms

Justin Solomon
Numerical Algorithms Book PDF

Author : Justin Solomon
Publisher : CRC Press
Page : 400 pages
File Size : 49,6 Mb
Release : 2015-06-24
Category : Computers
ISBN : 9781482251890

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Numerical Algorithms by Justin Solomon Pdf

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Software for Algebraic Geometry

Michael E. Stillman,Nobuki Takayama,Jan Verschelde
Software for Algebraic Geometry Book PDF

Author : Michael E. Stillman,Nobuki Takayama,Jan Verschelde
Publisher : Springer Science & Business Media
Page : 176 pages
File Size : 40,7 Mb
Release : 2008-05-29
Category : Mathematics
ISBN : 9780387781334

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Software for Algebraic Geometry by Michael E. Stillman,Nobuki Takayama,Jan Verschelde Pdf

Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms. This volume reflects the workshop “Software for Algebraic Geometry” held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications.

Computer Algebra in Scientific Computing

Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 419 pages
File Size : 43,5 Mb
Release : 2017-09-07
Category : Computers
ISBN : 9783319663203

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Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf

This book constitutes the proceedings of the 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017, held in Beijing, China, in September 2017. The 28 full papers presented in this volume were carefully reviewed and selected from 33 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.

Iterative Methods for Linear and Nonlinear Equations

C. T. Kelley
Iterative Methods for Linear and Nonlinear Equations Book PDF

Author : C. T. Kelley
Publisher : SIAM
Page : 169 pages
File Size : 40,7 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 9780898713527

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Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley Pdf

Mathematics of Computing -- Numerical Analysis.