Introduction To Numerical Continuation Methods PDF Download
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| Author | : Eugene L. Allgower |
| Publisher | : SIAM |
| Total Pages | : 409 |
| Release | : 2003-01-01 |
| Genre | : Mathematics |
| ISBN | : 089871544X |
Download Introduction to Numerical Continuation Methods Book in PDF, ePub and Kindle
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.
| Author | : Eugene L. Allgower |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 402 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642612571 |
Download Numerical Continuation Methods Book in PDF, ePub and Kindle
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.
| Author | : Bernd Krauskopf |
| Publisher | : Springer |
| Total Pages | : 399 |
| Release | : 2007-11-06 |
| Genre | : Science |
| ISBN | : 1402063563 |
Download Numerical Continuation Methods for Dynamical Systems Book in PDF, ePub and Kindle
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.
| Author | : Willy J. F. Govaerts |
| Publisher | : SIAM |
| Total Pages | : 384 |
| Release | : 2000-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898719543 |
Download Numerical Methods for Bifurcations of Dynamical Equilibria Book in PDF, ePub and Kindle
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.
| Author | : Hannes Uecker |
| Publisher | : SIAM |
| Total Pages | : 380 |
| Release | : 2021-08-19 |
| Genre | : Mathematics |
| ISBN | : 1611976618 |
Download Numerical Continuation and Bifurcation in Nonlinear PDEs Book in PDF, ePub and Kindle
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.
| Author | : Hans Petter Langtangen |
| Publisher | : Springer Nature |
| Total Pages | : 395 |
| Release | : 2019-09-26 |
| Genre | : Mathematics |
| ISBN | : 3030237885 |
Download Introduction to Numerical Methods for Variational Problems Book in PDF, ePub and Kindle
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.
| Author | : Uri M. Ascher |
| Publisher | : SIAM |
| Total Pages | : 574 |
| Release | : 2011-07-14 |
| Genre | : Mathematics |
| ISBN | : 0898719976 |
Download A First Course in Numerical Methods Book in PDF, ePub and Kindle
Offers students a practical knowledge of modern techniques in scientific computing.
| Author | : Justin Solomon |
| Publisher | : CRC Press |
| Total Pages | : 400 |
| Release | : 2015-06-24 |
| Genre | : Computers |
| ISBN | : 1482251892 |
Download Numerical Algorithms Book in PDF, ePub and Kindle
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
| Author | : Peter Stark |
| Publisher | : Simon & Schuster Books For Young Readers |
| Total Pages | : 356 |
| Release | : 1970 |
| Genre | : Mathematics |
| ISBN | : |
Download Introduction to Numerical Methods Book in PDF, ePub and Kindle
This text is for an introductory course in what is commonly called numerical analysis, numerical methods, or even numerical calculus. While it parallels the development in Course B4 on Numerical Calculus in the proposed Curriculum in Computer Science issued by the Association for Computing Machinery, this book is designed for any science or engineering student who has completed his first course in calculus, and who has at least a passing knowledge of elementary computer programming in FORTRAN. This is a practical book for the student who, in addition to seeing the theory of numerical methods, also likes to see the results; the predominant emphasis is on specific methods and computer solutions. It often points out where the theory departs from practice, and it illustrates each method of computer solution by an actual computer program and its results.
| Author | : Eugene L. Allgower |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 788 |
| Release | : 1990-04-03 |
| Genre | : Mathematics |
| ISBN | : 9780821896945 |
Download Computational Solution of Nonlinear Systems of Equations Book in PDF, ePub and Kindle
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.
