Numerical Continuation and Bifurcation in Nonlinear PDEs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Continuation and Bifurcation in Nonlinear PDEs write by Hannes Uecker. This book was released on 2021-08-19. Numerical Continuation and Bifurcation in Nonlinear PDEs available 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.
Introduction to Numerical Continuation Methods
Introduction to Numerical Continuation Methods - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Numerical Continuation Methods write by Eugene L. Allgower. This book was released on 2003-01-01. Introduction to Numerical Continuation Methods available 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.
Numerical Continuation Methods for Dynamical Systems
Numerical Continuation Methods for Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Continuation Methods for Dynamical Systems write by Bernd Krauskopf. This book was released on 2007-11-06. Numerical Continuation Methods for Dynamical Systems available 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.
Numerical Methods for Bifurcations of Dynamical Equilibria
Numerical Methods for Bifurcations of Dynamical Equilibria - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Methods for Bifurcations of Dynamical Equilibria write by Willy J. F. Govaerts. This book was released on 2000-01-01. Numerical Methods for Bifurcations of Dynamical Equilibria available 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.
Continuation and Bifurcations: Numerical Techniques and Applications
Continuation and Bifurcations: Numerical Techniques and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Continuation and Bifurcations: Numerical Techniques and Applications write by Dirk Roose. This book was released on 1990-08-31. Continuation and Bifurcations: Numerical Techniques and Applications available in PDF, EPUB and Kindle. Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989
