Perturbation Methods Bifurcation Theory And Computer Algebra

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Perturbation Methods, Bifurcation Theory and Computer Algebra

Richard H. Rand,Dieter Armbruster
Perturbation Methods Bifurcation Theory and Computer Algebra Book PDF

Author : Richard H. Rand,Dieter Armbruster
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210603

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Perturbation Methods, Bifurcation Theory and Computer Algebra by Richard H. Rand,Dieter Armbruster Pdf

Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.

Topics in Nonlinear Dynamics with Computer Algebra

R.H. Rand
Topics in Nonlinear Dynamics with Computer Algebra Book PDF

Author : R.H. Rand
Publisher : CRC Press
Page : 244 pages
File Size : 49,5 Mb
Release : 1994-04-14
Category : Mathematics
ISBN : 2884491139

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Topics in Nonlinear Dynamics with Computer Algebra by R.H. Rand Pdf

First published in 1994. Routledge is an imprint of Taylor & Francis, an informa company.

Multiple Scale and Singular Perturbation Methods

J.K. Kevorkian,J.D. Cole
Multiple Scale and Singular Perturbation Methods Book PDF

Author : J.K. Kevorkian,J.D. Cole
Publisher : Springer Science & Business Media
Page : 642 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239680

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Multiple Scale and Singular Perturbation Methods by J.K. Kevorkian,J.D. Cole Pdf

This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.

Computer Algebra in Scientific Computing

Vladimir P. Gerdt,Wolfram Koepf,Ernst W. Mayr,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : Vladimir P. Gerdt,Wolfram Koepf,Ernst W. Mayr,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 443 pages
File Size : 50,7 Mb
Release : 2013-08-15
Category : Computers
ISBN : 9783319022970

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Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Ernst W. Mayr,Evgenii V. Vorozhtsov Pdf

This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.

Random Perturbation Methods with Applications in Science and Engineering

Anatoli V. Skorokhod,Frank C. Hoppensteadt,Habib D. Salehi
Random Perturbation Methods with Applications in Science and Engineering Book PDF

Author : Anatoli V. Skorokhod,Frank C. Hoppensteadt,Habib D. Salehi
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 54,7 Mb
Release : 2007-06-21
Category : Mathematics
ISBN : 9780387224466

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Random Perturbation Methods with Applications in Science and Engineering by Anatoli V. Skorokhod,Frank C. Hoppensteadt,Habib D. Salehi Pdf

This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.

Computer Algebra Methods for Equivariant Dynamical Systems

Karin Gatermann
Computer Algebra Methods for Equivariant Dynamical Systems Book PDF

Author : Karin Gatermann
Publisher : Springer
Page : 163 pages
File Size : 46,8 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540465195

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Computer Algebra Methods for Equivariant Dynamical Systems by Karin Gatermann Pdf

This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.

Elements of Applied Bifurcation Theory

Yuri A. Kuznetsov
Elements of Applied Bifurcation Theory Book PDF

Author : Yuri A. Kuznetsov
Publisher : Springer Science & Business Media
Page : 529 pages
File Size : 43,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475724219

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Elements of Applied Bifurcation Theory by Yuri A. Kuznetsov Pdf

A solid basis for anyone studying the dynamical systems theory, providing the necessary understanding of the approaches, methods, results and terminology used in the modern applied-mathematics literature. Covering the basic topics in the field, the text can be used in a course on nonlinear dynamical systems or system theory. Special attention is given to efficient numerical implementations of the developed techniques, illustrated by several examples from recent research papers. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used, making this book suitable for advanced undergraduate or graduate students in applied mathematics, as well as for researchers in other disciplines who use dynamical systems as model tools in their studies.

Computer Algebra in Scientific Computing

V.G. Ganzha,E.W. Mayr,E.V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : V.G. Ganzha,E.W. Mayr,E.V. Vorozhtsov
Publisher : Springer
Page : 460 pages
File Size : 54,8 Mb
Release : 2007-09-04
Category : Computers
ISBN : 9783540751878

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Computer Algebra in Scientific Computing by V.G. Ganzha,E.W. Mayr,E.V. Vorozhtsov Pdf

This book constitutes the refereed proceedings of the 10th International Workshop on Computer Algebra in Scientific Computing, CASC 2007, held in Bonn, Germany, in September 2007. The volume is dedicated to Professor Vladimir P. Gerdt on the occasion of his 60th birthday. The papers cover not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms.

Elements of Applied Bifurcation Theory

Yuri Kuznetsov
Elements of Applied Bifurcation Theory Book PDF

Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
Page : 648 pages
File Size : 52,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475739787

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Elements of Applied Bifurcation Theory by Yuri Kuznetsov Pdf

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Singularities and Groups in Bifurcation Theory

Martin Golubitsky,David G. Schaeffer
Singularities and Groups in Bifurcation Theory Book PDF

Author : Martin Golubitsky,David G. Schaeffer
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 40,6 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461250340

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Singularities and Groups in Bifurcation Theory by Martin Golubitsky,David G. Schaeffer Pdf

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.

Computer Algebra in Scientific Computing CASC’99

Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing CASC 99 Book PDF

Author : Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642602184

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Computer Algebra in Scientific Computing CASC’99 by Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov Pdf

The development of powerful computer algebra systems has considerably ex tended the scope of problems of scientific computing which can now be solved successfully with the aid of computers. However, as the field of applications of computer algebra in scientific computing becomes broader and more complex, there is a danger of separation between theory, systems, and applications. For this reason, we felt the need to bring together the researchers who now ap ply the tools of computer algebra for the solution of problems in scientific computing, in order to foster new and closer interactions. CASC'99 is the second conference devoted to applications of computer al gebra in scientific computing. The first conference in this sequence, CASC'98, was held 20-24 April 1998 in St. Petersburg, Russia. This volume contains revised versions of the papers submitted by the par ticipants and accepted by the program committee after a thorough reviewing process. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scien tific computing: symbolic-numeric analysis and solving differential equations, efficient computations with polynomials, groups, matrices and other related objects, special purpose programming environments, application to physics, mechanics, optics and to other areas. In particular, a significant group of papers deals with applications of com puter algebra methods for the solution of current problems in group theory, which mostly arise in mathematical physics.

Perturbation Methods in Science and Engineering

Reza N. Jazar
Perturbation Methods in Science and Engineering Book PDF

Author : Reza N. Jazar
Publisher : Springer Nature
Page : 584 pages
File Size : 52,5 Mb
Release : 2021-07-12
Category : Technology & Engineering
ISBN : 9783030734626

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Perturbation Methods in Science and Engineering by Reza N. Jazar Pdf

Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems.

Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations

Charles Li,Stephen Wiggins
Invariant Manifolds and Fibrations for Perturbed Nonlinear Schr dinger Equations Book PDF

Author : Charles Li,Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 177 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461218388

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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations by Charles Li,Stephen Wiggins Pdf

In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds. Their techniques are based on an infinite dimensional generalisation of the graph transform and can be viewed as an infinite dimensional generalisation of Fenichels results. As such, they may be applied to a broad class of infinite dimensional dynamical systems.

Imperfect Bifurcation in Structures and Materials

Kiyohiro Ikeda,Kazuo Murota
Imperfect Bifurcation in Structures and Materials Book PDF

Author : Kiyohiro Ikeda,Kazuo Murota
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 47,9 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475736977

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Imperfect Bifurcation in Structures and Materials by Kiyohiro Ikeda,Kazuo Murota Pdf

Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

Bifurcations in Hamiltonian Systems

Henk Broer,Igor Hoveijn,Gerton Lunter,Gert Vegter
Bifurcations in Hamiltonian Systems Book PDF

Author : Henk Broer,Igor Hoveijn,Gerton Lunter,Gert Vegter
Publisher : Springer
Page : 178 pages
File Size : 50,5 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9783540363989

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Bifurcations in Hamiltonian Systems by Henk Broer,Igor Hoveijn,Gerton Lunter,Gert Vegter Pdf

The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.