Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations

Number of pages644
PublisherBerlin : Springer
Edition2nd ed.
  • Springer Series in Computational Mathematics; 31
Publication date2006

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. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.

  • Hamiltonian and reversible systems
  • Differential equations on manifolds
  • Geometric numerical integration
  • Symplectic and symmetric methods
Citation (ISO format)
HAIRER, Ernst, LUBICH, Christian, WANNER, Gerhard. Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations. 2nd ed. Berlin : Springer, 2006. (Springer Series in Computational Mathematics) doi: 10.1007/3-540-30666-8
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