常微分方程和微分代数方程的计算机方法

ListofFigures

ListofTables

Preface

PartⅠ：Introduction

1OrdinaryDifferentialEquations

1.1IVPs

1.2BVPs

1.3Differential-AlgebraicEquations

1.4FamiliesofApplicationProblems

1.5DynamicalSystems

1.6Notation

PartⅡ：InitialValueProblems

2OnProblemStability

2.1TestEquationandGeneralDefinitions

2.2Linear，Constant-CoefficientSystems

2.3Linear，Variable-CoefficientSystems

2.4NonlinearProblems

2.5HamiltonianSystems

2.6NotesandReferences

2.7Exercises

3BasicMethods，BasicConcepts

3.1ASimpleMethod：ForwardEuler

3.2Convergence，Accuracy，Consistency，andO-Stability

3.3AbsoluteStability

3.4Stiffness：BackwardEuler

3.4.1BackwardEuler

3.4.2SolvingNonlinearEquations

3.5A-Stability，StiffDecay

3.6Symmetry：TrapezoidalMethod

3.7RoughProblems

3.8Software，Notes，andReferences

3.8.1Notes

3.8.2Software

3.9Exercises

4One-StepMethods

4.1TheFirstRunge-KuttaMethods

4.2GeneralFormulationofRunge-KuttaMethods

4.3Convergence，O-Stability，andOrderforRunge-KuttaMethods

4.4RegionsofAbsoluteStabilityforExplicitRunge-KuttaMethods

4.5ErrorEstimationandControl

4.6SensitivitytoDataPerturbations

4.7ImplicitRunge-KuttaandCollocationMethods

4.7.1ImplicitRunge-KuttaMethodsBasedonCollocation

4.7.2ImplementationandDiagonallyImplicitMethods...

4.7.3OrderReduction

4.7.4MoreonImplementationandSinglyImplicitRungeKuttaMethods

4.8Software，Notes，andReferences

4.8.1Notes

4.8.2Software

4.9Exercises

5LinearMultistepMethods

5.1TheMostPopularMethods

5.1.1AdamsMethods

5.1.2BDF

5.1.3InitialValuesforMultistepMethods

5.2Order，O-Stability，andConvergence

5.2.1Order

5.2.2Stability：DifferenceEquationsandtheRootCondition

5.2.3O-StabilityandConvergence

5.3AbsoluteStability

5.4ImplementationofhnplicitLinearMultistepMethods

5.4.1FunctionalIteration

5.4.2Predictor-CorrectorMethods

5.4.3ModifiedNewtonIteration

5.5DesigningMultistepGeneral-PurposeSoftware

5.5.1VariableStep-SizeFormulae

5.5.2EstimatingandControllingtheLocalError

5.5.3ApproximatingtheSolutionatOff-StepPoints

5.6Software，Notes，andReferences

5.6.1Notes

5.6.2Software

5.7Exercises

PartⅢ：BoundaryValueProblems

6MoreBoundaryValueProblemTheoryandApplications

6.1LinearBVPsandGreensFunction.

6.2StabilityofBVPs

6.3BVPStiffness

6.4SomeReformulationTricks

6.5NotesandReferences

6.6Exercises

7Shooting

7.1Shooting：ASimpleMethodandItsLimitations

7.1.1Difficulties

7.2MultipleShooting

7.3Software，Notes，andReferences

7.3.1Notes

7.3.2Software

7.4Exercises

8FiniteDifferenceMethodsforBoundaryValueProblems

8.1MidpointandTrapezoidalMethods

8.1.1SolvingNonlinearProblems：Quasi-Linearization

8.1.2Consistency，O-Stability，andConvergence

8.2SolvingtheLinearEquations

8.3Higher-OrderMethods

8.3.1Collocation

8.3.2AccelerationTechniques

8.4MoreonSolvingNonlinearProblems

8.4.1DampedNewton

8.4.2ShootingforInitialGuesses

8.4.3Continuation

8.5ErrorEstimationandMeshSelection

8.6VeryStiffProblems

8.7Decoupling

8.8Software，Notes，andReferences

8.8.1Notes

8.8.2Software

8.9Exercises

PartⅣ：Differential-AlgebraicEquations

9MoreonDifferential-AlgebraicEquations

9.1IndexandMathematicalStructure

9.1.1SpecialDAEForms

9.1.2DAEStability

9.2IndexReductionandStabilization：ODEwithInvariant

9.2.1ReformulationofHigher-IndexDAEs

9.2.2ODEswithInvariants

9.2.3StateSpaceFormulation

9.3ModelingwithDAEs

9.4NotesandReferences

9.5Exercises

10NumericalMethodsforDifferential-AlgebraicEquations

10.1DirectDiscretizationMethods

10.1.1ASimpleMethod：BackwardEuler

10.1.2BDFandGeneralMultistepMethods

10.1.3RadauCollocationandImplicitRunge-KuttaMethods

10.1.4PracticalDifficulties

10.1.5SpecializedRunge-KuttaMethodsforHessenbergIndex-2DAEs

10.2MethodsforODEsonManifolds

10.2.1StabilizationoftheDiscreteDynamicalSystem

10.2.2ChoosingtheStabilizationMatrixF

10.3Software，Notes，andReferences

10.3.1Notes

10.3.2Software

10.4Exercises

Bibliography

Index

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