Download or read book Symplectic Integration of Constrained Hamiltonian Systems by Runge Kutta Methods written by Sebastian Reich and published by . This book was released on 1993 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Again it turns out that those partitioned Runge-Kutta methods which are symplectic for unconstrained systems can be applied to constrained Hamiltonian systems. We show that, in contrast to implicit Runge-Kutta methods, the class of symplectic partitioned Runge-Kutta methods includes methods that also preserve the constraints. In the third part of the paper we discuss constrained Hamiltonian systems with separable Hamiltonian from a Lie algebraic point of view. This approach not only provides a different approach to the numerical integration of Hamiltonian systems but also allows for a straightforward backward error analysis."
Download or read book Symplectic Partitioned Runge Kutta Methods for Constrained Hamiltonian Systems written by L. Jay and published by . This book was released on 1993 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symplectic Partitioned Runge Kutta Methods for Constrained Hamiltonian Systems written by Laurent-Olivier Jay and published by . This book was released on 1993 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symplectic Integration of Constrained Hamiltonian Systems by Rung Kutta Methods written by S. Reich and published by . This book was released on 1993 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sympkectic Integration of Constrained Hamiltonian Systems by Runge Kutta Methods written by Sebastian Reich and published by . This book was released on 1993 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Numerical Integration written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Almost Symplectic Runge Kutta Schemes for Hamiltonian Systems written by and published by . This book was released on 2004 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic Runge-Kutta schemes for the integration of general Hamiltonian systems are implicit. In practice one has to solve the implicit algebraic equations using some iterative approximation method, in which case the resulting integration scheme is no longer symplectic. In this paper we first analyze the preservation of the symplectic structure under two popular approximation schemes, fixed-point iteration and Newton's method, respectively. Error bounds for the symplectic structure are established when N fixed-point iterations or N iterations of Newton's method are used. The implications of these results for the implementation of symplectic methods are discussed and then explored through extensive numerical examples. Numerical comparisons with non-symplectic Runge-Kutta methods and pseudo-symplectic methods are also presented.
Download or read book Symplectic Geometric Algorithms for Hamiltonian Systems written by Kang Feng and published by Springer Science & Business Media. This book was released on 2010-10-18 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Numerical Hamiltonian Problems written by J.M. Sanz-Serna and published by Courier Dover Publications. This book was released on 2018-06-13 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced text explores mathematical problems that occur frequently in physics and other sciences. Topics include symplectic integration, symplectic order conditions, available symplectic methods, numerical experiments, properties of symplectic integrators. 1994 edition.
Download or read book Simulating Hamiltonian Dynamics written by Benedict Leimkuhler and published by Cambridge University Press. This book was released on 2004 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.
Download or read book Symplectic Geometry and Topology written by Yakov Eliashberg and published by American Mathematical Soc.. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Download or read book Symplectic Integration of Constrained Hamiltonian Systems written by Benedict Leimkuhler and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Acta Numerica 2003 Volume 12 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2003-09-15 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: An annual volume presenting substantive survey articles in numerical mathematics and scientific computing.
Download or read book Mathematical Approaches to Biomolecular Structure and Dynamics written by Jill P. Mesirov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES TO BIOMOLECULAR STRUCTURE AND DYNAMICS is one of the two volumes based on the proceedings of the 1994 IMA Sum mer Program on "Molecular Biology" and comprises Weeks 3 and 4 of the four-week program. Weeks 1 and 2 appeared as Volume 81: Genetic Mapping and DNA Sequencing. We thank Jill P. Mesirov, Klaus Schulten, and De Witt Sumners for organizing Weeks 3 and 4 of the workshop and for editing the proceedings. We also take this opportunity to thank the National Institutes of Health (NIH) (National Center for Human Genome Research), the National Science Foundation (NSF) (Biological Instrumen tation and Resources), and the Department of Energy (DOE), whose fi nancial support made the summer program possible. A vner Friedman Robert Gulliver v PREFACE The revolutionary progress in molecular biology within the last 30 years opens the way to full understanding of the molecular structures and mech anisms of living organisms. Interdisciplinary research in mathematics and molecular biology is driven by ever growing experimental, theoretical and computational power. The mathematical sciences accompany and support much of the progress achieved by experiment and computation as well as provide insight into geometric and topological properties of biomolecular structure and processes. This volume consists of a representative sample of the papers presented during the last two weeks of the month-long Institute for Mathematics and Its Applications Summer 1994 Program in Molecular Biology.
Download or read book Classical and Quantum Dynamics of Constrained Hamiltonian Systems written by Heinz J. Rothe and published by World Scientific. This book was released on 2010 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. The book is comprehensive and well-illustrated with examples, enables graduate students to follow the literature on this subject without much problems, and to perform research in this field.
Download or read book Integration Algorithms and Classical Mechanics written by Jerrold E. Marsden, George W. Patrick, and William F. Shadwick and published by American Mathematical Soc.. This book was released on with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the late Juan Carlos Simo, this volume contains the proceedings of a workshop held at the Fields Institute in October 1993. The articles focus on current algorithms for the integration of mechanical systems, from systems in celestial mechanics to coupled rigid bodies to fluid mechanics. The scope of the articles ranges from symplectic integration methods to energy-momentum methods and related themes.
Download or read book A Concise Introduction to Geometric Numerical Integration written by Sergio Blanes and published by CRC Press. This book was released on 2017-11-22 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
