Symplectic Geometric Algorithms For Hamiltonian Systems PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Symplectic Geometric Algorithms For Hamiltonian Systems PDF full book. Access full book title Symplectic Geometric Algorithms For Hamiltonian Systems.
Author | : Kang Feng |
Publisher | : Springer Science & Business Media |
Total Pages | : 690 |
Release | : 2010-10-18 |
Genre | : Mathematics |
ISBN | : 3642017770 |
Download Symplectic Geometric Algorithms for Hamiltonian Systems Book in PDF, ePub and Kindle
"Symplectic Geometric Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development of numerical methodology for Hamiltonian systems is well motivated. Were it successful, it would imply wide-ranging applications.
Author | : Kang Feng |
Publisher | : Springer |
Total Pages | : 676 |
Release | : 2014-04-14 |
Genre | : Mathematics |
ISBN | : 9783642443664 |
Download Symplectic Geometric Algorithms for Hamiltonian Systems Book in PDF, ePub and Kindle
"Symplectic Geometric Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development of numerical methodology for Hamiltonian systems is well motivated. Were it successful, it would imply wide-ranging applications.
Author | : Ernst Hairer |
Publisher | : Springer Science & Business Media |
Total Pages | : 526 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662050188 |
Download Geometric Numerical Integration Book in PDF, ePub and Kindle
This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.
Author | : Sergio Blanes |
Publisher | : CRC Press |
Total Pages | : 233 |
Release | : 2017-11-22 |
Genre | : Mathematics |
ISBN | : 1482263440 |
Download A Concise Introduction to Geometric Numerical Integration Book in PDF, ePub and Kindle
Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.
Author | : Tudor Ratiu |
Publisher | : Springer |
Total Pages | : 552 |
Release | : 1991-08-16 |
Genre | : Mathematics |
ISBN | : |
Download The Geometry of Hamiltonian Systems Book in PDF, ePub and Kindle
The papers in this volume are an outgrowth of some of the lectures and informal discussions that took place during the workshop on the geometry of Hamiltonian systems, held at the MSRI in Berkeley in June of 1989. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, numerical simulations and dynamical systems in general. The articles are of differing lengths and scopes; some are research announcements while others are surveys of particularly active areas of interest where the results can only be found in scattered research articles and preprints. In- cluded in the book is A.T. Fomenko's survey of the classification of integrable systems.
Author | : Tudor Ratiu |
Publisher | : |
Total Pages | : 527 |
Release | : 1991 |
Genre | : Hamiltonian systems |
ISBN | : 9783540976080 |
Download The Geometry of Hamiltonian Systems Book in PDF, ePub and Kindle
Author | : Vladimir Gerdjikov |
Publisher | : Springer Science & Business Media |
Total Pages | : 645 |
Release | : 2008-06-02 |
Genre | : Science |
ISBN | : 3540770534 |
Download Integrable Hamiltonian Hierarchies Book in PDF, ePub and Kindle
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
Author | : Helmut Hofer |
Publisher | : Springer Nature |
Total Pages | : 1158 |
Release | : 2022-12-05 |
Genre | : Mathematics |
ISBN | : 3031191110 |
Download Symplectic Geometry Book in PDF, ePub and Kindle
Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Author | : Xinyuan Wu |
Publisher | : Springer Science & Business Media |
Total Pages | : 244 |
Release | : 2013-02-02 |
Genre | : Technology & Engineering |
ISBN | : 364235338X |
Download Structure-Preserving Algorithms for Oscillatory Differential Equations Book in PDF, ePub and Kindle
Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory problems in applied sciences and engineering. The book discusses novel advances in the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving methods, etc. for oscillatory differential equations. The work is intended for scientists, engineers, teachers and students who are interested in structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing University; Xiong You is an associate professor at Nanjing Agricultural University; Bin Wang is a joint Ph.D student of Nanjing University and University of Cambridge.
Author | : A.V. Bolsinov |
Publisher | : CRC Press |
Total Pages | : 752 |
Release | : 2004-02-25 |
Genre | : Mathematics |
ISBN | : 0203643429 |
Download Integrable Hamiltonian Systems Book in PDF, ePub and Kindle
Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,