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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 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.
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Previews available in: English
Subjects
Mathematics, Numerical analysis, Global analysis (Mathematics), Mathematical physics, Number systems, Mathematical analysis, Mathematical & computational, Applied, Mathematics & statistics -> mathematics -> mathematics general, Physical & earth sciences -> physics -> mathematical physics, Scm14050, Scm12007, Scp19005, Scp19013, Scp19021, Scm31000, Suco11649, 3640, 3076, 2998, 5270, 3021Showing 3 featured editions. View all 3 editions?
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1
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
Sep 02, 2009, Springer
paperback
3540818324 9783540818328
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2
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
2006, Springer London, Limited
in English
3540306668 9783540306665
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3
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
2002, Springer Berlin Heidelberg
electronic resource :
in English
366205020X 9783662050200
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