Discrete Mechanics Geometric Integration And Lie Butcher Series

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Discrete Mechanics, Geometric Integration and Lie–Butcher Series

Kurusch Ebrahimi-Fard,María Barbero Liñán
Discrete Mechanics Geometric Integration and Lie Butcher Series Book PDF

Author : Kurusch Ebrahimi-Fard,María Barbero Liñán
Publisher : Springer
Page : 361 pages
File Size : 48,9 Mb
Release : 2018-11-05
Category : Mathematics
ISBN : 9783030013974

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Discrete Mechanics, Geometric Integration and Lie–Butcher Series by Kurusch Ebrahimi-Fard,María Barbero Liñán Pdf

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.

Computation and Combinatorics in Dynamics, Stochastics and Control

Elena Celledoni,Giulia Di Nunno,Kurusch Ebrahimi-Fard,Hans Zanna Munthe-Kaas
Computation and Combinatorics in Dynamics Stochastics and Control Book PDF

Author : Elena Celledoni,Giulia Di Nunno,Kurusch Ebrahimi-Fard,Hans Zanna Munthe-Kaas
Publisher : Springer
Page : 734 pages
File Size : 45,5 Mb
Release : 2019-01-13
Category : Mathematics
ISBN : 9783030015930

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Computation and Combinatorics in Dynamics, Stochastics and Control by Elena Celledoni,Giulia Di Nunno,Kurusch Ebrahimi-Fard,Hans Zanna Munthe-Kaas Pdf

The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.

Geometric Science of Information

Frank Nielsen,Frédéric Barbaresco
Geometric Science of Information Book PDF

Author : Frank Nielsen,Frédéric Barbaresco
Publisher : Springer Nature
Page : 670 pages
File Size : 53,7 Mb
Release : 2023-07-31
Category : Computers
ISBN : 9783031382994

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Geometric Science of Information by Frank Nielsen,Frédéric Barbaresco Pdf

This book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.

Algebra and Applications 2

Abdenacer Makhlouf
Algebra and Applications 2 Book PDF

Author : Abdenacer Makhlouf
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 42,8 Mb
Release : 2021-12-07
Category : Mathematics
ISBN : 9781119880905

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Algebra and Applications 2 by Abdenacer Makhlouf Pdf

This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the second of three volumes specifically focusing on algebra and its applications. Algebra and Applications 2 centers on the increasing role played by combinatorial algebra and Hopf algebras, including an overview of the basic theories on non-associative algebras, operads and (combinatorial) Hopf algebras. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Alongside the focal topic of combinatorial algebra and Hopf algebras, non-associative algebraic structures in iterated integrals, chronological calculus, differential equations, numerical methods, control theory, non-commutative symmetric functions, Lie series, descent algebras, Butcher groups, chronological algebras, Magnus expansions and Rota–Baxter algebras are explored. Algebra and Applications 2 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.

From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory

Fritz Gesztesy,Andrei Martinez-Finkelshtein
From Operator Theory to Orthogonal Polynomials Combinatorics and Number Theory Book PDF

Author : Fritz Gesztesy,Andrei Martinez-Finkelshtein
Publisher : Springer Nature
Page : 388 pages
File Size : 42,5 Mb
Release : 2021-11-11
Category : Mathematics
ISBN : 9783030754259

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From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory by Fritz Gesztesy,Andrei Martinez-Finkelshtein Pdf

The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. García, L.G. Garza, F. Gesztesy, D. Gómez-Ullate, Y. Grandati, F.A. Grünbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellán, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velázquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.

Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics

D.H. Sattinger,O.L. Weaver
Lie Groups and Algebras with Applications to Physics Geometry and Mechanics Book PDF

Author : D.H. Sattinger,O.L. Weaver
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 45,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475719109

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Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics by D.H. Sattinger,O.L. Weaver Pdf

This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.

The Structure of Compact Groups

Karl H. Hofmann,Sidney A. Morris
The Structure of Compact Groups Book PDF

Author : Karl H. Hofmann,Sidney A. Morris
Publisher : Walter de Gruyter GmbH & Co KG
Page : 1034 pages
File Size : 44,7 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783110695991

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The Structure of Compact Groups by Karl H. Hofmann,Sidney A. Morris Pdf

This book is designed both as a textbook for high-level graduate courses and as a reference for researchers who need to apply the structure and representation theory of compact groups. A gentle introduction to compact groups and their representation theory is followed by self-contained courses on linear and compact Lie groups, and on locally compact abelian groups. This fourth edition was updated with the latest developments in the field.

Geometric Numerical Integration

Ernst Hairer,Christian Lubich,Gerhard Wanner
Geometric Numerical Integration Book PDF

Author : Ernst Hairer,Christian Lubich,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 526 pages
File Size : 40,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662050187

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Geometric Numerical Integration by Ernst Hairer,Christian Lubich,Gerhard Wanner Pdf

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.

Integration Algorithms and Classical Mechanics

Jerrold E. Marsden, George W. Patrick, and William F. Shadwick
Integration Algorithms and Classical Mechanics Book PDF

Author : Jerrold E. Marsden, George W. Patrick, and William F. Shadwick
Publisher : American Mathematical Soc.
Page : 260 pages
File Size : 41,7 Mb
Release : 2024-06-30
Category : Differentiable dynamical systems
ISBN : 0821871188

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Integration Algorithms and Classical Mechanics by Jerrold E. Marsden, George W. Patrick, and William F. Shadwick Pdf

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.

A Concise Introduction to Geometric Numerical Integration

Sergio Blanes,Fernando Casas
A Concise Introduction to Geometric Numerical Integration Book PDF

Author : Sergio Blanes,Fernando Casas
Publisher : CRC Press
Page : 233 pages
File Size : 42,6 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781482263442

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A Concise Introduction to Geometric Numerical Integration by Sergio Blanes,Fernando Casas Pdf

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.

Symplectic Geometric Algorithms for Hamiltonian Systems

Kang Feng,Mengzhao Qin
Symplectic Geometric Algorithms for Hamiltonian Systems Book PDF

Author : Kang Feng,Mengzhao Qin
Publisher : Springer Science & Business Media
Page : 690 pages
File Size : 47,5 Mb
Release : 2010-10-18
Category : Mathematics
ISBN : 9783642017773

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Symplectic Geometric Algorithms for Hamiltonian Systems by Kang Feng,Mengzhao Qin Pdf

"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.

Algebra and Applications 2

Abdenacer Makhlouf
Algebra and Applications 2 Book PDF

Author : Abdenacer Makhlouf
Publisher : John Wiley & Sons
Page : 338 pages
File Size : 52,7 Mb
Release : 2021-12-29
Category : Mathematics
ISBN : 9781789450187

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Algebra and Applications 2 by Abdenacer Makhlouf Pdf

This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the second of three volumes specifically focusing on algebra and its applications. Algebra and Applications 2 centers on the increasing role played by combinatorial algebra and Hopf algebras, including an overview of the basic theories on non-associative algebras, operads and (combinatorial) Hopf algebras. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Alongside the focal topic of combinatorial algebra and Hopf algebras, non-associative algebraic structures in iterated integrals, chronological calculus, differential equations, numerical methods, control theory, non-commutative symmetric functions, Lie series, descent algebras, Butcher groups, chronological algebras, Magnus expansions and Rota–Baxter algebras are explored. Algebra and Applications 2 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.

Integration Algorithms and Classical Mechanics

Jerrold E. Marsden,William Francis Shadwick,George William Patrick,W. F. Shadwick
Integration Algorithms and Classical Mechanics Book PDF

Author : Jerrold E. Marsden,William Francis Shadwick,George William Patrick,W. F. Shadwick
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 40,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821802595

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Integration Algorithms and Classical Mechanics by Jerrold E. Marsden,William Francis Shadwick,George William Patrick,W. F. Shadwick Pdf

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.

Highly Oscillatory Problems

Bjorn Engquist
Highly Oscillatory Problems Book PDF

Author : Bjorn Engquist
Publisher : Cambridge University Press
Page : 254 pages
File Size : 42,7 Mb
Release : 2009-07-02
Category : Mathematics
ISBN : 9780521134439

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Highly Oscillatory Problems by Bjorn Engquist Pdf

Review papers from experts in areas of active research into highly oscillatory problems, with an emphasis on computation.

Foundations of Computational Mathematics

Ronald A. DeVore,Arieh Iserles,Endre Süli
Foundations of Computational Mathematics Book PDF

Author : Ronald A. DeVore,Arieh Iserles,Endre Süli
Publisher : Cambridge University Press
Page : 418 pages
File Size : 45,8 Mb
Release : 2001-05-17
Category : Mathematics
ISBN : 0521003490

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Foundations of Computational Mathematics by Ronald A. DeVore,Arieh Iserles,Endre Süli Pdf

Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.