國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Geometric integrators for differenti...

SpringerLink (Online service)

Geometric integrators for differential equations with highly oscillatory solutions

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometric integrators for differential equations with highly oscillatory solutionsby Xinyuan Wu, Bin Wang.
作者:	Wu, Xinyuan.
其他作者:	Wang, Bin.
出版者:	Singapore :Springer Singapore :2021.
面頁冊數:	xviii, 499 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Differential equationsNumerical solutions.
電子資源:	https://doi.org/10.1007/978-981-16-0147-7
ISBN:	9789811601477$q(electronic bk.)

Geometric integrators for differential equations with highly oscillatory solutions
Wu, Xinyuan.

Geometric integrators for differential equations with highly oscillatory solutions[electronic resource] /by Xinyuan Wu, Bin Wang. - Singapore :Springer Singapore :2021. - xviii, 499 p. :ill., digital ;24 cm.

1 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.

The 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.

ISBN: 9789811601477$q(electronic bk.)

Standard No.: 10.1007/978-981-16-0147-7doiSubjects--Topical Terms:

199018
Differential equations
--Numerical solutions.

LC Class. No.: QA372

Dewey Class. No.: 515.35

Geometric integrators for differential equations with highly oscillatory solutions
LDR:03971nmm a2200325 a 4500 001 609644
003 DE-He213
005 20210928163326.0
006 m d
007 cr nn 008maaau
008 220222s2021 si s 0 eng d
020 $a 9789811601477$q(electronic bk.)
020 $a 9789811601460$q(paper)
024 7 $a 10.1007/978-981-16-0147-7 $2 doi
035 $a 978-981-16-0147-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA372
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515.35 $2 23
090 $a QA372 $b .W959 2021
100 1 $a Wu, Xinyuan. $3 732925
245 1 0 $a Geometric integrators for differential equations with highly oscillatory solutions $h [electronic resource] / $c by Xinyuan Wu, Bin Wang.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2021.
300 $a xviii, 499 p. : $b ill., digital ; $c 24 cm.
505 0 $a 1 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.
520 $a The 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.
650 0 $a Differential equations $x Numerical solutions. $3 199018
650 0 $a Geometric analysis. $3 509359
650 1 4 $a Analysis. $3 273775
650 2 4 $a Numerical Analysis. $3 275681
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Vibration, Dynamical Systems, Control. $3 274667
700 1 $a Wang, Bin. $3 260378
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-981-16-0147-7
950 $a Mathematics and Statistics (SpringerNature-11649)