振荡微分方程的保结构算法（英文版）

图书标准信息

• 作者 Xinyuan、Xiong、Bin Wang 著
• 出版社 科学出版社
• 出版时间 2013-03
• 版次 01
• ISBN 9787030355201
• 定价 78.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 236页
• 字数 250千字
• 正文语种 英语

【内容简介】

　　Theobjectiveofthismonographistostudystructure-preservingalgorithmsforoscillatoryproblemsthatariseinawiderangeoffieldssuchasastronomy，molecu-lardynamics，classicalmechanics，quantummechanics，chemistry，biologyanden-gineering.Suchproblemscanoftenbemodeledbyinitialvalueproblemsofsecond-orderdifferentialequationswithalineartermcharacterizingtheoscillatorystruc-tureofthesystems.Sincegeneral-purposehighorderRunge-Kutta（RK）methods，Runge-Kutta-Nystrom（RKN）methods，andlinearmultistepmethods（LMM）can-notrespectthespecialstructuresofoscillatoryproblemsinlong-termintegration，innovativeintegratorshavetobedesigned.Thismonographsystematicallydevelopstheoriesandmethodsforsolvingsecond-orderdifferentialequationswithoscillatorysolutions.

【目录】

1　Runge-Kutta（-Nystrom）MethodsforOscillatoryDifferentialEquations
1.1　RKMethods,RootedTrees,B-SeriesandOrderConditions
1.2　RKNMethods,NystromTreesandOrderConditions
1.2.1　FormulationoftheScheme
1.2.2　NystromTreesandOrderConditions
1.2.3　TheSpecialCaseinAbsenceoftheDerivative
1.3　DispersionandDissipationofRK（N）Methods
1.3.1　RKMethods
1.3.2　RKNMethods
1.4　SymplecticMethodsforHamiltonianSystems
1.5　CommentsonStructure-PreservingAlgorithmsforOscillatoryProblems
References

2　ARKNMethods
2.1　TraditionalARKNMethods
2.1.1　FormulationoftheScheme
2.1.2　OrderConditions
2.2　SymplecticARKNMethods
2.2.1　SymplecticityConditionsforARKNIntegrators
2.2.2　ExistenceofSymplecticARKNIntegrators
2.2.3　PhaseandStabilityPropertiesofMethodSARKNls2
2.2.4　NonexistenceofSymmetricARKNMethods
2.2.5　NumericalExperiments
2.3　MultidimensionaIARKNMethods
2.3.1　FormulationoftheScheme
2.3.2　OrderConditions
2.3.3　PracticalMultidimensionalARKNMethods
References

3　ERKNMethods
3.1　ERKNMethods
3.1.1　FormulationofMultidimensionalERKNMethods
3.1.2　SpecialExtendedNystromTreeTheory
3.1.3　OrderConditions
3.2　EFRKNMethodsandERKNMethods
3.2.1　One-DimensionaICase
3.2.2　MultidimensionalCase
3.3　ERKNMethodsforSecond-OrderSystemswithVariablePrincipaIFrequencyMatrix
3.3.　AnalysisThroughanEquivalentSystem
3.3.2　TowardsERKNMethods
3.3.3　Numericallllustrations
References

4　SymplecticandSymmetricMultidimensionaIERKNMethods
4.1　SymplecticityandSymmetryConditionsforMultidimensionalERKNlntegrators
4.1.1　SymmetryConditions
4.1.2　SymplecticityConditions
4.2　ConstructionofExplicitSSMERKNIntegrators
4.2.1　TwoTwo-StageSSMERKNlntegratorsofOrderTwo
4.2.2　AThree-StageSSMERKNIntegratorofOrderFour
4.2.3　StabilityandPhasePropertiesofSSMERKNIntegrators
4.3　NumericalExperiments
4.4　ERKNMethodsforLong-TermIntegrationofOrbitalProblems
4.5　SymplecticERKNMethodsforTime-DependentSecond-OrderSystems
4.5.1　EquivalentExtendedAutonomousSystemsforNon-autonomousSystems
4.5.2　SymplecticERKNMethodsforTime-DependentHamiltonianSystems
4.6　ConcludingRemarks
References

5　Two-StepMultidimensionaIERKNMethods
5.1　TheScheifeleTwo-StepMethods
5.2FormulationofTSERKNMethods
5.3OrderConditions
5.3.1　B-SeriesonSENT
5.3.2One-StepFormulation
5.3.3OrderConditions
5.4　ConstructionofExplicitTSERKNMethods
5.4.1　AMethodwithTwoFunctionEvaluationsperStep
5.4.2　MethodswithThreeFunctionEvaluationsperStep
5.5　StabilityandPhasePropertiesoftheTSERKNMethods
……

6　AdaptedFalkner-TypeMethods
7　Energy-PreservingERKNMethods
8　EffectiveMethodsforHighlyOscillatorySecond-OrderNonlinearDifferentiaIEquations
9　ExtendedLeap-FrogMethodsforHanultonianWaveEquations
AppendixFirstandSecondSymposiumsonStructure-PreservingAlgorithmsforDifferentialEquations,August2011,June2012,Nanjing
Index