000			03507cam a22004934a 4500
999			_c3284
001			16095817
003			EC-UrYT
005			20200513144338.0
006			s||||gr|||| 00| 00
008			100218s2010 gw a b 001 0 eng
010			_a 2010922987
020			_a9783642051579 (softcover)
040			_aDLC _cDLC _dEC-UrYT
041			_aeng
082			_221 _a515.352
100	1		_aHairer, E. _q(Ernst) _98904
245	1	0	_aGeometric numerical integration : _bstructure-preserving algorithms for ordinary differential equations / _cErnst Hairer, Christian Lubich, Gerhard Wanner.
250			_aSecond edition
264	3	4	_aHeidelberg ; _aNew York : _bSpringer, _cc2010.
300			_axvii, 644 pages : _billustrations ; _c25 cm.
490			_aSpringer series in computational mathematics _x0179-3632 ; _v31
500			_aInclude index
504			_aIncludes bibliographical references (p. [617]-636) and index.
505	2		_aExamples and numerical experiments -- Numerical integrators -- Order conditions, trees and B-series -- Conservation of first integrals and methods on manifolds -- Symmetric integration and reversibility -- Symplectic integration of Hamiltonian systems -- Non-canonical Hamiltonian systems -- Structure-preserving implementation -- Backward error analysis and structure preservation -- Hamiltonian perturbation theory and symplectic integrators -- Reversible perturbation theory and symmetric integrators -- Dissipative perturbed Hamiltonian and reversible systems -- Oscillatory diffential equations with constant high frequencies -- Oscillatory differential equations with varying high frequencies -- Dynamics of multistep methods.
520	3		_a 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.
650		0	_aDifferential equations _9528 _xNumerical solutions
650		0	_aHamiltonian systems. _92965
650		0	_aNumerical integration _98906
650		0	_aMathematical physics _9540
650		0	_aNumerical analysis _9504
700	1		_aLubich, Christian _d1959- _98907 _eauthor
700	1		_aWanner, Gerhard _98908 _eauthor
856	4	2	_3Publisher description _uhttp://www.loc.gov/catdir/enhancements/fy1317/2010922987-d.html
856	4	1	_3Table of contents only _uhttp://www.loc.gov/catdir/enhancements/fy1402/2010922987-t.html
942			_2ddc _cLIBRO