《振盪微分方程的保結構算法》是2013年科學出版社出版的圖書，作者是Xinyuan Wu、Xiong You、Bin Wang 。
基本介紹
- 書名：振盪微分方程的保結構算法
- 作者：Xinyuan Wu，Xiong You，Bin Wang
- ISBN：9787030355201
- 頁數：236
- 定價：78.00元
- 出版社：科學出版社
- 出版時間：2013-4
內容簡介,目錄,
內容簡介
《振盪微分方程的保結構算法(英文版)》內容簡介：Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for secondorder oscillatory differential equations by using theoretical analysis and numerical validation.Structure-preserving algorithms for differential equations,especially for oscillatory differential equations,play an important role in the accurate simulation of oscillatory problems in applied sciences and engineering.The book discusses novel advances in the ARKN,ERKN,two-step ERKN,Falkner-type and energy-preserving methods,etc.for oscillatory differential equations.
目錄
1 Runge-Kutta （-Nystrom） Methods for Oscillatory Differentia lEquations
1.1 RK Methods, Rooted Trees, B-Series and Order Conditions
1.2 RKN Methods, Nystrom Trees and Order Conditions
1.2.1 Formulation ofthe Scheme
1.2.2 NystromTrees and Order Conditions
1.2.3 The SpecialCasein Absence ofthe Derivative
1.3 Dispersion and Dissipation ofRK（N） Methods
1.3.1 RKMethods
1.3.2 RKNMethods
1.4 Symplectic Methods for Hamiltonian Systems
1.5 Comments on Structure-Preserving Algorithms for Oscillatory Problems
References
2 ARKNMethods
2.1 TraditionalARKNMethods
2.1.1 Formulationofthe Scheme
2.1.2 OrderConditions
2.2 Symplectic ARKN Methods
2.2.1 SymplecticityConditionsforARKNIntegrators
2.2.2 Existence ofSymplectic ARKNIntegrators
2.2.3 Phase and Stability Properties ofMethod SARKNls2
2.2.4 Nonexistence ofSymmetric ARKN Methods
2.2.5 NumericalExperiments
2.3 MultidimensionaIARKN Methods
2.3.1 Formulation ofthe Scheme
2.3.2 OrderConditions
2.3.3 PracticalMultidimensionalARKN Methods
References
3 ERKNMethods
3.1 ERKNMethods
3.1.1 FormulationofMultidimensionalERKNMethods
3.1.2 SpecialExtended Nystrom Tree Theory
3.1.3 OrderConditions
3.2 EFRKN Methods and ERKN Methods
3.2.1 One-DimensionaICase
3.2.2 MultidimensionalCase
3.3 ERKN Methods for Second-Order Systems with Variable PrincipaIFrequencyMatrix
3.3. Analysis Through an Equivalent System
3.3.2 Towards ERKNMethods
3.3.3 Numericallllustrations
References
4 Symplectic and Symmetric MultidimensionaIERKN Methods
4.1 Symplecticity and Symmetry Conditions for Multidimensional ERKNlntegrators
4.1.1 Symmetry Conditions
4.1.2 SymplecticityConditions
4.2 Construction ofExplicit SSMERKNIntegrators
4.2.1 Two Two-Stage SSMERKNlntegrators of Order Two
4.2.2 AThree-StageSSMERKNIntegratorofOrderFour
4.2.3 Stability and Phase Properties ofSSMERKNIntegrators
4.3 NumericalExperiments
4.4 ERKN Methods for Long-Term Integration of Orbital Problems
4.5 Symplectic ERKN Methods for Time-Dependent Second-Order Systems
4.5.1 Equivalent Extended Autonomous Systems for Non- autonomous Systems
4.5.2 Symplectic ERKN Methods for Time-Dependen tHamiltonianSystems
4.6 ConcludingRemarks
References
5 Two-Step MultidimensionaIERKN Methods
5.1 The ScheifeleTwo-Step Methods
5.2 FormulationofTSERKNMethods
5.3 OrderConditions
5.3.1 B-SeriesonSENT
5.3.2 One-StepFormulation
5.3.3 OrderConditions
5.4 ConstructionofExplicitTSERKNMethods
5.4.1 A Method with Two Function Evaluations per Step
5.4.2 Methods with Three Function Evaluations per Step
5.5 Stability and Phase Properties ofthe TSERKN Methods
……
6 Adapted Falkner-Type Methods
7 Energy-Preserving ERKN Methods
8 Effective Methods for Highly Oscillatory Second-Order Nonlinear DifferentiaIEquations
9 Extended Leap-Frog Methods for Hanultonian Wave Equations
Appendix First and Second Symposiums on Structure-Preserving Algorithms for Differential Equations, August 2011, June 2012, Nanjing
Index
1.1 RK Methods, Rooted Trees, B-Series and Order Conditions
1.2 RKN Methods, Nystrom Trees and Order Conditions
1.2.1 Formulation ofthe Scheme
1.2.2 NystromTrees and Order Conditions
1.2.3 The SpecialCasein Absence ofthe Derivative
1.3 Dispersion and Dissipation ofRK（N） Methods
1.3.1 RKMethods
1.3.2 RKNMethods
1.4 Symplectic Methods for Hamiltonian Systems
1.5 Comments on Structure-Preserving Algorithms for Oscillatory Problems
References
2 ARKNMethods
2.1 TraditionalARKNMethods
2.1.1 Formulationofthe Scheme
2.1.2 OrderConditions
2.2 Symplectic ARKN Methods
2.2.1 SymplecticityConditionsforARKNIntegrators
2.2.2 Existence ofSymplectic ARKNIntegrators
2.2.3 Phase and Stability Properties ofMethod SARKNls2
2.2.4 Nonexistence ofSymmetric ARKN Methods
2.2.5 NumericalExperiments
2.3 MultidimensionaIARKN Methods
2.3.1 Formulation ofthe Scheme
2.3.2 OrderConditions
2.3.3 PracticalMultidimensionalARKN Methods
References
3 ERKNMethods
3.1 ERKNMethods
3.1.1 FormulationofMultidimensionalERKNMethods
3.1.2 SpecialExtended Nystrom Tree Theory
3.1.3 OrderConditions
3.2 EFRKN Methods and ERKN Methods
3.2.1 One-DimensionaICase
3.2.2 MultidimensionalCase
3.3 ERKN Methods for Second-Order Systems with Variable PrincipaIFrequencyMatrix
3.3. Analysis Through an Equivalent System
3.3.2 Towards ERKNMethods
3.3.3 Numericallllustrations
References
4 Symplectic and Symmetric MultidimensionaIERKN Methods
4.1 Symplecticity and Symmetry Conditions for Multidimensional ERKNlntegrators
4.1.1 Symmetry Conditions
4.1.2 SymplecticityConditions
4.2 Construction ofExplicit SSMERKNIntegrators
4.2.1 Two Two-Stage SSMERKNlntegrators of Order Two
4.2.2 AThree-StageSSMERKNIntegratorofOrderFour
4.2.3 Stability and Phase Properties ofSSMERKNIntegrators
4.3 NumericalExperiments
4.4 ERKN Methods for Long-Term Integration of Orbital Problems
4.5 Symplectic ERKN Methods for Time-Dependent Second-Order Systems
4.5.1 Equivalent Extended Autonomous Systems for Non- autonomous Systems
4.5.2 Symplectic ERKN Methods for Time-Dependen tHamiltonianSystems
4.6 ConcludingRemarks
References
5 Two-Step MultidimensionaIERKN Methods
5.1 The ScheifeleTwo-Step Methods
5.2 FormulationofTSERKNMethods
5.3 OrderConditions
5.3.1 B-SeriesonSENT
5.3.2 One-StepFormulation
5.3.3 OrderConditions
5.4 ConstructionofExplicitTSERKNMethods
5.4.1 A Method with Two Function Evaluations per Step
5.4.2 Methods with Three Function Evaluations per Step
5.5 Stability and Phase Properties ofthe TSERKN Methods
……
6 Adapted Falkner-Type Methods
7 Energy-Preserving ERKN Methods
8 Effective Methods for Highly Oscillatory Second-Order Nonlinear DifferentiaIEquations
9 Extended Leap-Frog Methods for Hanultonian Wave Equations
Appendix First and Second Symposiums on Structure-Preserving Algorithms for Differential Equations, August 2011, June 2012, Nanjing
Index
