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 : 40,9 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 : 54,9 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.

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 : 40,5 Mb
Release : 2007-11-06
Category : Science
ISBN : 9781402063565

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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 : 48,6 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 : 55,9 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.

Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

Abel Gomes,Irina Voiculescu,Joaquim Jorge,Brian Wyvill,Callum Galbraith
Implicit Curves and Surfaces Mathematics Data Structures and Algorithms Book PDF

Author : Abel Gomes,Irina Voiculescu,Joaquim Jorge,Brian Wyvill,Callum Galbraith
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 54,6 Mb
Release : 2009-05-12
Category : Computers
ISBN : 9781848824065

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Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms by Abel Gomes,Irina Voiculescu,Joaquim Jorge,Brian Wyvill,Callum Galbraith Pdf

Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications. Divided into two parts, the first introduces the mathematics of implicit curves and surfaces, as well as the data structures suited to store their sampled or discrete approximations, and the second deals with different computational methods for sampling implicit curves and surfaces, with particular reference to how these are applied to functions in 2D and 3D spaces.

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 : 52,6 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.

Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics

V.I. Shalashilin,E. B. Kuznetsov
Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics Book PDF

Author : V.I. Shalashilin,E. B. Kuznetsov
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 40,7 Mb
Release : 2003-09-30
Category : Mathematics
ISBN : 1402015429

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Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics by V.I. Shalashilin,E. B. Kuznetsov Pdf

The optimal continuation parameter provides the best conditions in a linearized system of equations at any moment of the continuation process. This is one of the first books in which the best parametrization is regarded systematically for a wide class of problems. It is of interest to scientists, specialists, and postgraduate students of applied and numerical mathematics and mechanics.

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 : 43,5 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.

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 : 55,8 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.

Numerical Algorithms

Justin Solomon
Numerical Algorithms Book PDF

Author : Justin Solomon
Publisher : CRC Press
Page : 400 pages
File Size : 51,6 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

Computational Solution of Nonlinear Systems of Equations

Eugene L. Allgower,Kurt Georg
Computational Solution of Nonlinear Systems of Equations Book PDF

Author : Eugene L. Allgower,Kurt Georg
Publisher : American Mathematical Soc.
Page : 788 pages
File Size : 54,7 Mb
Release : 1990-04-03
Category : Mathematics
ISBN : 0821896946

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Computational Solution of Nonlinear Systems of Equations by Eugene L. Allgower,Kurt Georg Pdf

Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.

Recipes for Continuation

Harry Dankowicz,Frank Schilder
Recipes for Continuation Book PDF

Author : Harry Dankowicz,Frank Schilder
Publisher : SIAM
Page : 585 pages
File Size : 43,8 Mb
Release : 2013-08-08
Category : Mathematics
ISBN : 9781611972566

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Recipes for Continuation by Harry Dankowicz,Frank Schilder Pdf

This book provides a comprehensive introduction to the mathematical methodology of parameter continuation. It develops a systematic formalism for constructing and implementing abstract representations of continuation problems with equal emphasis on theoretical rigor, algorithm development and software engineering. The book demonstrates the use of fully developed toolbox templates for boundary-value problems to the analysis of periodic orbits, quasi-periodic invariant tori, and connecting orbits between equilibria and/or periodic orbits. The book contains extensive and fully-worked examples that illustrate the application of the MATLAB-based Computational Continuation Core (COCO) to cutting-edge research in applied dynamical systems. Many exercises and open-ended projects on both theoretical and algorithmic aspects of the material are provided, suitable for self-study and course assignments. It is intended for students and teachers of nonlinear dynamics and engineering at the advanced undergraduate or first-year graduate level, as well as practitioners engaged in modeling dynamical systems or software development.

A First Course in Numerical Methods

Uri M. Ascher,Chen Greif
A First Course in Numerical Methods Book PDF

Author : Uri M. Ascher,Chen Greif
Publisher : SIAM
Page : 574 pages
File Size : 40,7 Mb
Release : 2011-07-14
Category : Mathematics
ISBN : 9780898719970

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A First Course in Numerical Methods by Uri M. Ascher,Chen Greif Pdf

Offers students a practical knowledge of modern techniques in scientific computing.

Newton Methods for Nonlinear Problems

Peter Deuflhard
Newton Methods for Nonlinear Problems Book PDF

Author : Peter Deuflhard
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 43,7 Mb
Release : 2005-01-13
Category : Mathematics
ISBN : 3540210997

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Newton Methods for Nonlinear Problems by Peter Deuflhard Pdf

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.