LEADER 01425nam0-22004691i-450- 001 990003714270403321 005 20001010 035 $a000371427 035 $aFED01000371427 035 $a(Aleph)000371427FED01 035 $a000371427 100 $a20000920d1936----km-y0itay50------ba 101 0 $aita 105 $ay-------001yy 200 1 $aAnnales de finances publiques comparees 205 $aPrima edizione 210 $aParigi$cDomat-Montchrestien$d1936 215 $a182p.$d23cm 710 02$aInstitut de droit comparé de l' université de paris$0381320 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990003714270403321 952 $aH01.241/1$b25228$fDECTS 952 $aH01.241/2$b25229$fDECTS 952 $aH01.241/3$b25230$fDECTS 952 $aH01.241/3.BS$b1947$fDECTS 952 $aH01.241/4$b1948$fDECTS 952 $aH01.241/4.BS$b17915$fDECTS 952 $aH01.241/4.TR$b25231$fDECTS 952 $aH01.241/5$b25232$fDECTS 952 $aH01.241/6$b2037$fDECTS 952 $aH01.241/6.BS$b03918$fDECTS 952 $aH01.241/7$b2038$fDECTS 952 $aH01.241/7.BS$b03919$fDECTS 952 $aH01.241/8$b03920$fDECTS 952 $aH01.241/8.BS$b2039$fDECTS 952 $aH01.241/9$b2040$fDECTS 952 $aH01.241/9.BS$b03921$fDECTS 959 $aDECTS 996 $aAnnales de finances publiques comparees$9500408 997 $aUNINA DB $aING01 LEADER 04760nam 22006015 450 001 9910503005503321 005 20251113183333.0 010 $a981-16-0147-X 024 7 $a10.1007/978-981-16-0147-7 035 $a(CKB)4100000012038691 035 $a(MiAaPQ)EBC6736352 035 $a(Au-PeEL)EBL6736352 035 $a(OCoLC)1272993474 035 $a(PPN)258056231 035 $a(DE-He213)978-981-16-0147-7 035 $a(EXLCZ)994100000012038691 100 $a20210928d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Integrators for Differential Equations with Highly Oscillatory Solutions /$fby Xinyuan Wu, Bin Wang 205 $a1st ed. 2021. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2021. 215 $a1 online resource (507 pages) 225 1 $aMathematics and Statistics Series 311 08$a981-16-0146-1 327 $a1 Oscillation-Preserving Integrators for Highly Oscillatory Systems of Second-Order ODEs -- 2 Continuous-Stage ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions -- 3 Stability and Convergence Analysis of ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions -- 4 Functionally-Fitted Energy-Preserving Integrators for Poisson Systems -- 5 Exponential Collocation Methods for Conservative or Dissipative Systems -- 6 Volume-Preserving Exponential Integrators -- 7 Global Error Bounds of One-Stage Explicit ERKN Integrators for Semilinear Wave Equations -- 8 Linearly-Fitted Conservative (Dissipative) Schemes for Nonlinear Wave Equations -- 9 Energy-Preserving Schemes for High-Dimensional Nonlinear KG Equations -- 10 High-Order Symmetric Hermite?Birkhoff Time Integrators for Semilinear KG Equations -- 11 Symplectic Approximations for Efficiently Solving Semilinear KG Equations -- 12 Continuous-Stage Leap-Frog Schemes for Semilinear Hamiltonian Wave Equations -- 13 Semi-Analytical ERKN Integrators for Solving High-Dimensional Nonlinear Wave Equations -- 14 Long-Time Momentum and Actions Behaviour of Energy-Preserving Methods for Wave Equations. 330 $aThe idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these equations cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this monograph is to explore further geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations. Facing challenging scientific computational problems, this book presents some new perspectives of the subject matter based on theoretical derivations and mathematical analysis, and provides high-performance numerical simulations. In order to show the long-time numerical behaviour of the simulation, all the integrators presented in this monograph have been tested and verified on highly oscillatory systems from a wide range of applications in the field of science and engineering. They are more efficient than existing schemes in the literature for differential equations that have highly oscillatory solutions. This book is useful to researchers, teachers, students and engineers who are interested in Geometric Integrators and their long-time behaviour analysis for differential equations with highly oscillatory solutions. . 410 0$aMathematics and Statistics Series 606 $aMathematical analysis 606 $aNumerical analysis 606 $aDynamics 606 $aAnalysis 606 $aNumerical Analysis 606 $aDynamical Systems 615 0$aMathematical analysis. 615 0$aNumerical analysis. 615 0$aDynamics. 615 14$aAnalysis. 615 24$aNumerical Analysis. 615 24$aDynamical Systems. 676 $a515.35 700 $aWu$b Xinyuan$0767990 701 $aWang$b Bin$0767991 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910503005503321 996 $aGeometric Integrators for Differential Equations with Highly Oscillatory Solutions$92568954 997 $aUNINA