Symplectic Integration of Constrained Hamiltonian Systems by Runge-Kutta Methods 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 Integration of Constrained Hamiltonian Systems by Runge-Kutta Methods PDF full book. Access full book title Symplectic Integration of Constrained Hamiltonian Systems by Runge-Kutta Methods by Sebastian Reich. Download full books in PDF and EPUB format.
Author: Sebastian Reich
Publisher:
ISBN:
Category : Hamiltonian systems
Languages : en
Pages : 24
Get Book Here
Book Description
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."
Author: Sebastian Reich
Publisher:
ISBN:
Category : Hamiltonian systems
Languages : en
Pages : 24
Get Book Here
Book Description
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."
Author: L. Jay
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
Get Book Here
Book Description
Author: S. Reich
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
Get Book Here
Book Description
Author: Laurent-Olivier Jay
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
Get Book Here
Book Description
Author: Sebastian Reich
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Ernst Hairer
Publisher: Springer Science & Business Media
ISBN: 3662050188
Category : Mathematics
Languages : en
Pages : 526
Get Book Here
Book Description
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:
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
Get Book Here
Book Description
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.
Author: Kang Feng
Publisher: Springer Science & Business Media
ISBN: 3642017770
Category : Mathematics
Languages : en
Pages : 690
Get Book Here
Book Description
"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: J.M. Sanz-Serna
Publisher: Courier Dover Publications
ISBN: 0486824101
Category : Mathematics
Languages : en
Pages : 225
Get Book Here
Book Description
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.
Author: Benedict Leimkuhler
Publisher: Cambridge University Press
ISBN: 9780521772907
Category : Mathematics
Languages : en
Pages : 464
Get Book Here
Book Description
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.
