000			03956nam a22005295i 4500
001			978-3-662-48156-1
003			DE-He213
005			20200420220216.0
007			cr nn 008mamaa
008			160302s2015 gw | s |||| 0|eng d
020			_a9783662481561 _9978-3-662-48156-1
024	7		_a10.1007/978-3-662-48156-1 _2doi
050		4	_aTA329-348
050		4	_aTA640-643
072		7	_aTBJ _2bicssc
072		7	_aMAT003000 _2bisacsh
082	0	4	_a519 _223
100	1		_aWu, Xinyuan. _eauthor.
245	1	0	_aStructure-Preserving Algorithms for Oscillatory Differential Equations II _h[electronic resource] / _cby Xinyuan Wu, Kai Liu, Wei Shi.
250			_a1st ed. 2015.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2015.
300			_aXV, 298 p. 55 illus., 11 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aMatrix-variation-of-constants formula -- Improved St �ormer-Verlet formulae with applications -- Improved Filon-type asymptotic methods for highly oscillatory differential equations -- Efficient energy-preserving integrators for multi-frequency oscillatory Hamiltonian systems -- An extended discrete gradient formula for multi-frequency oscillatory Hamiltonian systems -- Trigonometric Fourier collocation methods for multi-frequency oscillatory systems -- Error bounds for explicit ERKN integrators for multi-frequency oscillatory systems -- Error analysis of explicit TSERKN methods for highly oscillatory systems -- Highly accurate explicit symplectic ERKN methods for multi-frequency oscillatory Hamiltonian systems -- Multidimensional ARKN methods for general multi-frequency oscillatory second-order IVPs -- A simplified Nystr�om-tree theory for ERKN integrators solving oscillatory systems -- An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations.
520			_aThis book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics and electronics. To accurately simulate the true behavior of such systems, a numerical algorithm must preserve as much as possible their key structural properties: time-reversibility, oscillation, symplecticity, and energy and momentum conservation. The book describes novel advances in RKN methods, ERKN methods, Filon-type asymptotic methods, AVF methods, and trigonometric Fourier collocation methods.  The accuracy and efficiency of each of these algorithms are tested via careful numerical simulations, and their structure-preserving properties are rigorously established by theoretical analysis. The book also gives insights into the practical implementation of the methods. This book is intended for engineers and scientists investigating oscillatory systems, as well as for teachers and students who are interested in structure-preserving algorithms for differential equations.
650		0	_aEngineering.
650		0	_aComputer mathematics.
650		0	_aPhysics.
650		0	_aApplied mathematics.
650		0	_aEngineering mathematics.
650	1	4	_aEngineering.
650	2	4	_aAppl.Mathematics/Computational Methods of Engineering.
650	2	4	_aTheoretical, Mathematical and Computational Physics.
650	2	4	_aComputational Science and Engineering.
700	1		_aLiu, Kai. _eauthor.
700	1		_aShi, Wei. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783662481554
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-662-48156-1
912			_aZDB-2-ENG
942			_cEBK
999			_c51622 _d51622