Geometric Numerical Integration
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Geometric Numerical Integration
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Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-18
Geometric Numerical Integration written by Ernst Hairer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-18 with Mathematics categories.
This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents a theory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.
A Concise Introduction To Geometric Numerical Integration
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Author : Sergio Blanes
language : en
Publisher: CRC Press
Release Date : 2017-11-22
A Concise Introduction To Geometric Numerical Integration written by Sergio Blanes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
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.
Geometric Numerical Integration
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Author : Ernst Hairer
language : en
Publisher: Springer Verlag
Release Date : 2006-02-22
Geometric Numerical Integration written by Ernst Hairer and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-22 with Mathematics categories.
This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents a theory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.
Geometric Numerical Integration
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Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Geometric Numerical Integration written by Ernst Hairer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. 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 many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.
Geometric Numerical Integration
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Author : Ernst Hairer
language : en
Publisher:
Release Date : 2014-01-15
Geometric Numerical Integration written by Ernst Hairer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Geometric Numerical Integration
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Author : Pui Sze Priscilla Tse
language : en
Publisher:
Release Date : 2007
Geometric Numerical Integration written by Pui Sze Priscilla Tse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Differential equations categories.
This result implies that B-series methods cannot preserve both volume and affine symmetries simultaneously for arbitrary systems. Lastly, we present a new fourth-order method which is symplectic, self-adjoint, and preserves the exact linearization at fixed points of an arbitrary Hamiltonian system. This method is based on the preprocessed vector field integrators, which is the concept of integrating a preprocessed version of the original vector field as opposed to direct integration. We find numerically that, for certain Hamiltonian systems, the global truncation error grows more slowly for this new preprocessed integrator than for other fourth-order integrators such as the non-symplectic Runge-Kutta method and the symplectic and self-adjoint Gauss method.
Geometric Numerical Integration Of Differential Equations
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Author : Reinout Quispel
language : en
Publisher:
Release Date : 2006
Geometric Numerical Integration Of Differential Equations written by Reinout Quispel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Special Issue On Geometric Numerical Integration Of Differential Equations
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Author :
language : en
Publisher:
Release Date : 2006
Special Issue On Geometric Numerical Integration Of Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations categories.
Discrete Mechanics Geometric Integration And Lie Butcher Series
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Author : Kurusch Ebrahimi-Fard
language : en
Publisher: Springer
Release Date : 2018-11-05
Discrete Mechanics Geometric Integration And Lie Butcher Series written by Kurusch Ebrahimi-Fard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.
This volume resulted from presentations given at the international “Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie–Butcher Series”, that took place at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid, Spain. It combines overview and research articles on recent and ongoing developments, as well as new research directions. Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowned experts in numerical analysis of differential equations, provide a compelling answer to this question. After this introductory chapter a collection of high-quality research articles aim at exploring recent and ongoing developments, as well as new research directions in the areas of geometric integration methods for differential equations, nonlinear systems interconnections, and discrete mechanics. One of the highlights is the unfolding of modern algebraic and combinatorial structures common to those topics, which give rise to fruitful interactions between theoretical as well as applied and computational perspectives. The volume is aimed at researchers and graduate students interested in theoretical and computational problems in geometric integration theory, nonlinear control theory, and discrete mechanics.
Geometric Numerical Integration For Optimisation
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Author : Erlend Skaldehaug Riis
language : en
Publisher:
Release Date : 2019
Geometric Numerical Integration For Optimisation written by Erlend Skaldehaug Riis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.