Special Issue On Geometric Numerical Integration Of Differential Equations
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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.
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.
Acta Numerica 2003 Volume 12
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-15
Acta Numerica 2003 Volume 12 written by Arieh Iserles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-15 with Juvenile Nonfiction categories.
An annual volume presenting substantive survey articles in numerical mathematics and scientific computing.
Structure Preserving Algorithms For Oscillatory Differential Equations
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Author : Xinyuan Wu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-02
Structure Preserving Algorithms For Oscillatory Differential Equations written by Xinyuan Wu 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 2013-02-02 with Technology & Engineering categories.
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.
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.
Recent Progress And Modern Challenges In Applied Mathematics Modeling And Computational Science
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Author : Roderick Melnik
language : en
Publisher: Springer
Release Date : 2017-09-05
Recent Progress And Modern Challenges In Applied Mathematics Modeling And Computational Science written by Roderick Melnik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-05 with Mathematics categories.
This volume is an excellent resource for professionals in various areas of applications of mathematics, modeling, and computational science. It focuses on recent progress and modern challenges in these areas. The volume provides a balance between fundamental theoretical and applied developments, emphasizing the interdisciplinary nature of modern trends and detailing state-of-the-art achievements in Applied Mathematics, Modeling, and Computational Science. The chapters have been authored by international experts in their respective fields, making this book ideal for researchers in academia, practitioners, and graduate students. It can also serve as a reference in the diverse selected areas of applied mathematics, modelling, and computational sciences, and is ideal for interdisciplinary collaborations.
Nbs Special Publication
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Author :
language : en
Publisher:
Release Date : 1965
Nbs Special Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Weights and measures categories.
Numerical Integration Of Differential Equations And Large Linear Systems
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Author : J. Hinze
language : en
Publisher: Springer
Release Date : 2006-11-15
Numerical Integration Of Differential Equations And Large Linear Systems written by J. Hinze and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Frattura Ed Integrit Strutturale Annals 2014
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Author : Luca Susmel
language : en
Publisher: Gruppo Italiano Frattura
Release Date : 2014-09-12
Frattura Ed Integrit Strutturale Annals 2014 written by Luca Susmel and has been published by Gruppo Italiano Frattura this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-12 with Technology & Engineering categories.
Current Challenges In Stability Issues For Numerical Differential Equations
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Author : Wolf-Jürgen Beyn
language : en
Publisher: Springer
Release Date : 2013-12-12
Current Challenges In Stability Issues For Numerical Differential Equations written by Wolf-Jürgen Beyn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-12 with Mathematics categories.
This volume addresses some of the research areas in the general field of stability studies for differential equations, with emphasis on issues of concern for numerical studies. Topics considered include: (i) the long time integration of Hamiltonian Ordinary DEs and highly oscillatory systems, (ii) connection between stochastic DEs and geometric integration using the Markov chain Monte Carlo method, (iii) computation of dynamic patterns in evolutionary partial DEs, (iv) decomposition of matrices depending on parameters and localization of singularities, and (v) uniform stability analysis for time dependent linear initial value problems of ODEs. The problems considered in this volume are of interest to people working on numerical as well as qualitative aspects of differential equations, and it will serve both as a reference and as an entry point into further research.