LEADER 04755nam 22006495 450 001 9910299673603321 005 20251116150047.0 010 $a3-662-48156-1 024 7 $a10.1007/978-3-662-48156-1 035 $a(CKB)3710000000616370 035 $a(EBL)4442027 035 $a(SSID)ssj0001653887 035 $a(PQKBManifestationID)16433294 035 $a(PQKBTitleCode)TC0001653887 035 $a(PQKBWorkID)14982629 035 $a(PQKB)10946702 035 $a(DE-He213)978-3-662-48156-1 035 $a(MiAaPQ)EBC4442027 035 $a(PPN)192769766 035 $a(EXLCZ)993710000000616370 100 $a20160302d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStructure-preserving algorithms for oscillatory differential equations II /$fby Xinyuan Wu, Kai Liu, Wei Shi 205 $a1st ed. 2015. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2015. 215 $a1 online resource (305 p.) 300 $aDescription based upon print version of record. 311 08$a3-662-48155-3 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aMatrix-variation-of-constants formula -- Improved St šormer-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 Nystršom-tree theory for ERKN integrators solving oscillatory systems -- An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations. 330 $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. 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aMathematical physics 606 $aComputer science$xMathematics 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aMathematical physics. 615 0$aComputer science$xMathematics. 615 14$aMathematical and Computational Engineering. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aComputational Science and Engineering. 676 $a620 700 $aWu$b Xinyuan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767990 702 $aLiu$b Kai$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aShi$b Wei$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910299673603321 996 $aStructure-Preserving Algorithms for Oscillatory Differential Equations II$92522065 997 $aUNINA