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010   $a981-10-9004-1
024 7 $a10.1007/978-981-10-9004-2
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035   $a(MiAaPQ)EBC5356807
035   $a(DE-He213)978-981-10-9004-2
035   $a(PPN)226695085
035   $a(EXLCZ)994100000003359795
100   $a20180419d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aRecent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations /$fby Xinyuan Wu, Bin Wang
205   $a1st ed. 2018.
210  1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2018.
215   $a1 online resource (356 pages)
311   $a981-10-9003-3 
327   $aFunctionally ?tted continuous ?nite element methods for oscillatory Hamiltonian system -- Exponential average-vector-?eld integrator for conservative or dissipative systems -- Exponential Fourier collocation methods for ?rst-order differential Equations -- Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems -- High-order symplectic and symmetric composition integrators for multi-frequency oscillatory Hamiltonian systems -- The construction of arbitrary order ERKN integrators via group theory -- Trigonometric collocation methods for multi-frequency and multidimensional oscillatory systems -- A compact tri-colored tree theory for general ERKN methods -- An integral formula adapted to different boundary conditions for arbitrarily high-dimensional nonlinear Klein-Gordon equations -- An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations -- Arbitrarily high-order time-stepping schemes for nonlinear Klein?Gordon equations -- An essential extension of the ?nite-energy condition for ERKN integrators solving nonlinear wave equations -- Index.
330   $aThe main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.
606   $aAlgorithms
606   $aComputational complexity
606   $aMathematics of Algorithmic Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/M13130
606   $aComplexity$3https://scigraph.springernature.com/ontologies/product-market-codes/T11022
615  0$aAlgorithms.
615  0$aComputational complexity.
615 14$aMathematics of Algorithmic Complexity.
615 24$aComplexity.
676   $a515.35
700   $aWu$b Xinyuan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767990
702   $aWang$b Bin$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910300123603321
996   $aRecent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations$91963847
997   $aUNINA