rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Geometric Numerical Integration
    sub title: Structure-Preserving Algorithms for Ordinary Differential Equations
  name:
    name part: Hairer, E. (Ernst)
    role:
      role term: creator
  name:
    name part: Wanner, Gerhard.
  name:
    name part: Lubich, Christian.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 2002
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xiii, 515 pages)
  abstract: 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.
  table of contents: I. Examples and Numerical Experiments -- II. Numerical Integrator -- III. Order-Conditions, Trees, and B-Series -- IV. Conservation of First Integrals and Methods on Manifolds -- V. Symmetric Integration and Reversibility -- VI. Symplectic Integration of Hamiltonian Systems -- VII. Further Topics in Structure Preservation. -- VIII. Structure-Preserving Implementation -- IX. Backward Error Analysis and Structure Preservation -- X. Hamiltonian Perturbation Theory and Symplectic Integrators -- XI. Reversible Perturbation Theory and Symmetric Integrators -- XII. Dissipatively Perturbed Hamiltonian and Reversible Systems -- XIII. Highly Oscillatory Differential Equations -- XIV. Dynamics of Multistep Methods -- Bibliography.
  note: by Ernst Hairer, Gerhard Wanner, Christian Lubich.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Numerical analysis
  subject:
    topic: Mathematical physics
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Mathematical physics
  subject:
    topic: Mathematics
  subject:
    topic: Numerical analysis
  classification: QA297-299.4
  classification: 518
  related item:
    title info:
      title: Springer series in computational mathematics ; 31
  identifier: 9783662050187 (electronic bk.)
  identifier: 3662050188 (electronic bk.)
  identifier: 9783662050200
  identifier: 366205020X
  identifier: 3662050188
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 130217
    record change date: 20260420211642.7
    record identifier: in00003560645
    language of cataloging:
      language term: eng