Author: Urs Kirchgraber
Publisher: Longman Scientific and Technical
ISBN: 9780582062689
Category : Differentiable dynamical systems
Languages : en
Pages : 89
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Book Description
The aim of this Research Note is to elucidate the behaviour of a dynamical system in the neighbourhood of a fixed point or invariant torus (in the case of a diffeomorphism) or an equilibrium (in the case of an ordinary differential equation). It is shown that the space has both a horizontal and vertical foliation. Each leaf in the vertical foliation consists of the initial points of those orbits which are asymptotic to a particular orbit on the centre-stable manifold. This structure leads to a linearization of the system.
Author: Urs Kirchgraber
Publisher:
ISBN: 9780608052359
Category :
Languages : en
Pages : 101
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Book Description
Author: Stephen Wiggins
Publisher: Springer Science & Business Media
ISBN: 1461243122
Category : Mathematics
Languages : en
Pages : 198
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Book Description
In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.
Author: D.F. Griffiths
Publisher: CRC Press
ISBN: 1000158055
Category : Mathematics
Languages : en
Pages : 293
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Book Description
This volume contains invited papers presented at the 15th Dundee Biennial Conference on Numerical Analysis held at the University of Dundee in June of 1993. The Dundee Conferences are important events in the numerical analysis calendar, and the papers published here represent accounts of recent research work by leading numerical analysts covering a wide range of fields of interest. The book is a valuable guide to the direction of current research in many areas of numerical analysis. It will be of particular interest to graduate students and research workers concerned with the theory and application of numerical methods for solving ordinary and partial differential equations.
Author: Saburou Saitoh
Publisher: CRC Press
ISBN: 1000158047
Category : Mathematics
Languages : en
Pages : 300
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Book Description
The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.
Author: G P Galdi
Publisher: CRC Press
ISBN: 1000941019
Category : Mathematics
Languages : en
Pages : 176
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Book Description
Including previously unpublished, original research material, this comprehensive book analyses topics of fundamental importance in theoretical fluid mechanics. The five papers appearing in this volume are centred around the mathematical theory of the Navier-Stokes equations (incompressible and compressible) and certain selected non-Newtonian modifications.
Author: James H Bramble
Publisher: Routledge
ISBN: 1351429868
Category : Mathematics
Languages : en
Pages : 175
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Book Description
Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.
Author: Yuan Xu
Publisher: CRC Press
ISBN: 1000117235
Category : Mathematics
Languages : en
Pages : 136
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Book Description
Presents a systematic study of the common zeros of polynomials in several variables which are related to higher dimensional quadrature. The author uses a new approach which is based on the recent development of orthogonal polynomials in several variables and differs significantly from the previous ones based on algebraic ideal theory. Featuring a great deal of new work, new theorems and, in many cases, new proofs, this self-contained work will be of great interest to researchers in numerical analysis, the theory of orthogonal polynomials and related subjects.
Author: B N Mandal
Publisher: CRC Press
ISBN: 1000115224
Category : Mathematics
Languages : en
Pages : 144
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Book Description
An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.
Author: Martin Hanke
Publisher: CRC Press
ISBN: 1351458337
Category : Mathematics
Languages : en
Pages : 143
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Book Description
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.
