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Geometric Numerical Integration : Structure-Preserving Algorithms for Ordinary Differential Equations /

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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...

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Bibliographic Details
Main Author: Hairer, E. (Ernst)
Corporate Author: SpringerLink (Online service)
Other Authors: Wanner, Gerhard, Lubich, Christian
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2002.
Series:Springer series in computational mathematics ; 31.
Subjects:
Mathematics.
Global analysis (Mathematics)
Numerical analysis.
Mathematical physics.
Electronic books.
Online Access:Connect to the full text of this electronic book
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.