常微分方程和微分代數方程的計算機方法

這本書包含了所有必要的物質上的兩個領域的領先，它提供了一個統一的初始值介紹在常微分方程以及微分代數equations.The方法邊界值問題的目的是在透徹理解的問題和實際計算方法。

基本介紹

• 中文名：常微分方程和微分代數方程的計算機方法
• 外文名：Ordinary differential equation and differential algebraic equation method of the computer
• 實質：強調基本理論和方法
• 例子：科學工程applications.Topics

內容簡介

Designed for those people who want to gain a practical knowledge of modern techniques，this book contains all the material necessary for a course on the nmnerical solution of differential equations.Written by two of the field's leading athorities，it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential algebraic equations.The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding a nextensive the orem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. 　This book is a practical and mathematically well informed introduction that emphasizes basic methods and theory，issues in the use and development of mathematical software，and examples from scientific engineering applications.Topics requiring an extensive amount of mathematical development，such as symplectic methods for Hamiltonian systems，are introduced，motivated，and included in the exercises，but a complete and rigorous mathematical presentation is referenced rather than included. 　This book is appropriate for senior undergraduate or beginning graduate students with a computational focus and practicing engineers and scientists who want to learn about computational differential equations.A beginning course in numerical analysis is needed，and a beginning course in ordinary differential equations would be helpful.

中文內容簡介

這些人誰想要獲得一個現代技術的實用知識的設計，它還涉及現有的軟體為什麼成功或失敗的原因。這本書強調基本理論和方法，數學軟體的使用和發展中的問題，並從科學工程applications.Topics的例子，如哈密頓系統的辛方法需要廣泛的數學發展的實際和數學靈通的引進，介紹，有上進心，包括在演習，但一個完整的和嚴格的數學演示，而不是引用包括。這本書是適當的高年級本科生或開始與計算重點和執業工程師和科學家要了解計算差equations.A的數值分析的開始當然是需要的研究生，並在常微分方程的開始當然會有所幫助。

圖書目錄

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

6.1LinearBVPsandGreen'sFunction'.

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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