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Thursday, July 9, 2020 | History

2 edition of Geometric Numerical Integration found in the catalog.

Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

by Ernst Hairer

  • 322 Want to read
  • 11 Currently reading

Published by Springer Berlin Heidelberg in Berlin, Heidelberg .
Written in English

    Subjects:
  • Mathematics,
  • Numerical analysis,
  • Global analysis (Mathematics),
  • Mathematical physics

  • About the Edition

    The subject of this book is numerical methods that preserve geometric properties of the flow of a differential equation: symplectic integrators for Hamiltonian systems, symmetric integrators for reversible systems, methods preserving first integrals and numerical methods on manifolds, including Lie group methods and integrators for constrained mechanical systems, and methods for problems with highly oscillatory solutions. A complete theory of symplectic and symmetric 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 and related perturbation theories. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.

    Edition Notes

    Statementby Ernst Hairer, Gerhard Wanner, Christian Lubich
    SeriesSpringer Series in Computational Mathematics -- 31, Springer Series in Computational Mathematics -- 31
    ContributionsWanner, Gerhard, Lubich, Christian
    Classifications
    LC ClassificationsQA297-299.4
    The Physical Object
    Format[electronic resource] :
    Pagination1 online resource (xiii, 515 p.)
    Number of Pages515
    ID Numbers
    Open LibraryOL27041007M
    ISBN 10366205020X, 3662050188
    ISBN 109783662050200, 9783662050187
    OCLC/WorldCa851368851

    Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations by Ernst Hairer, Dr. Gerhard Wanner, Christian Lubich starting at $ Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations has 1 available editions to buy at Half Price Books Marketplace. Numerical integration is the term used for a number of methods to find an approximation for an cal integration has also been called often, it is not possible to solve integration analytically, for example when the data consists of a number of distinct measurements, or when the antiderivative is not known, and it is difficult, impractical or impossible to find it.

    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 Author: Benedict Leimkuhler, Sebastian Reich. ( views) Numerical Analysis: Theory and Application by Jan Awrejcewicz - InTech, The book introduces theoretical approach to numerical analysis as well as applications of various numerical methods to solving numerous theoretical and engineering problems. The book is useful for both theoretical and applied research.

    Numerical Complex Analysis. This note covers the following topics: Fourier Analysis, Least Squares, Normwise Convergence, The Discrete Fourier Transform, The Fast Fourier Transform, Taylor Series, Contour integration, Laurent series, Chebyshev series, Signal smoothing and root finding, Differentiation and integration, Spectral methods, Ultraspherical spectral methods, Functional analysis. What is geometric numerical integration? First elementary examples and numerical methods Classical paradigm of numerical integration Towards a new paradigm: geometric numerical integration Symplectic integration Illustration: the Kepler problem What is to be treated in this book (and what is not) Classical integrators and preservation of properties Taylor series methods Runge-Kutta methods.


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Geometric Numerical Integration by Ernst Hairer Download PDF EPUB FB2

Geometric Numerical Integration deals with the foundations, examples and actual applications of geometric integrators in various fields of research, and there is a lot on the more abstract theory of numerical mathematics, the classification of algorithms, provided with lots of mathematical and physical background needed to understand what is Cited by: 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.

Geometric Numerical Integration | SpringerLink. The material of the book is organized in sections which are self-contained, so that one can dip into the book to learn a particular topic. A person interested in geometrical numerical integration will find this book extremely useful." (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol.

(20), ). Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics Book 31) - Kindle edition by Hairer, Ernst, Lubich, Christian, Wanner, Gerhard.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Geometric Numerical /5(5). The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.

Keywords Hamiltonian and reversible systems Numerical integration calculus differential equation differential equations on manifolds dynamics geometric numerical integration.

Numerical integration Geometric Numerical Integration book are convenient tools to solve them. Geometric integrators (Hairer et al. ) can preserve one or more physical/geometric properties of these systems. The properties. 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. 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.

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.

Ernst Hairer is the author of Geometric Numerical Integration ( avg rating, 8 ratings, 0 reviews, published ), Solving Ordinary Differential Equa /5(31).

Pendulum example. We can motivate the study of geometric integrators by considering the motion of a pendulum. Assume that we have a pendulum whose bob has mass = and whose rod is massless of the acceleration due to gravity to by the angular displacement of the rod from the vertical, and by () the pendulum's momentum.

The Hamiltonian of the system, the sum of its. Book Description. 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.

Book Reference Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations HAIRER, Ernst, LUBICH, Christian, WANNER, Gerhard Abstract Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions.

Numerical Geometric Integration Ernst Hairer Univ ersit e de Gen ev Marc h Section de math ematiques Case p ostale CH Gen ev e Con ten ts I Examples and Numerical Exp erimen ts 1 I.1 Tw o-Dimensional Problems.

1 I.2 Kepler's Problem and the Outer Solar System. 4 I.3 Molecular Dynamics. 8 I.4 Highly Oscillatory Problems. 11 I   Geometric numerical integration (GNI) is a relatively recent discipline, concerned with the computation of differential equations while retaining their geometric and structural features : Ernst Hairer.

"[A Concise Introduction to Geometric Numerical Integration] is highly recommended for graduate students, postgraduate researchers, and researchers interested in beginning study in.

Get this from a library. Geometric numerical integration: structure-preserving algorithms for ordinary differential equations. [E Hairer; Christian Lubich; Gerhard Wanner] -- 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.

The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration.

Positivity of the phase space, Poisson structure of the flows, conservation of invariants that characterize the continuous ecological models are. 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. Buy Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics) 2 by Hairer, Ernst, Lubich, Christian, Wanner, Gerhard (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on /5(3). Buy Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics) 2nd Print by Hairer, Ernst, Lubich, Christian, Wanner, Gerhard (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible s: 3.In mathematics, and more specifically in numerical analysis, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) is a technique for approximating the definite integral.

∫ (). The trapezoidal rule works by approximating the region under the graph of the function as a trapezoid and calculating its area.

It follows that ∫ ≈ (−) ⋅ + ().Abstract. Geometric integration is a field that was invented “too late, ” and this book is an impressive record of a decade of catching up. It could have been invented at any time since Newton.

1 It could have been invented inwith “a marvellous paper, short, clear, elegant, written in one week, submitted for publication—and never published ” [4].