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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.
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Previews available in: English
Subjects
Differential equations, Numerical integration, Hamiltonian systems, Numerical solutions, Differential equations, numerical solutions, Differential equations--numerical solutions, Biomathematics, Global analysis (mathematics), Mathematical physics, Mathematics, Numerical analysis, Physics, Qa299.3 .h35 2006, Quantum physics, Mathematical equations - integral, Numerical analysis & solutions, Mathematical equations - differential, BiologyEdition | Availability |
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1
Geometric numerical integration: structure-preserving algorithms for ordinary differential equations
2010, Springer
in English
- 2nd ed.
364205157X 9783642051579
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2
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics)
April 2006, Springer
Hardcover
in English
- 2nd ed. edition
3540306633 9783540306634
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3
Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations
October 15, 2004, Springer
Hardcover
in English
- 1st ed. 2002. Corr. 2nd printing edition
3540430032 9783540430032
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