这本书包含了所有必要的物质上的两个领域的领先，它提供了一个统一的初始值介绍在常微分方程以及微分代数equations.The方法边界值问题的目的是在透彻理解的问题和实际计算方法。

内容简介

中文内容简介

图书目录

内容简介

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.

中文内容简介

这些人谁想要获得一个现代技术的实用知识的设计，它还涉及现有的软件为什么成功或失败的原因。这本书强调基本理论和方法，数学软件的使用和发展中的问题，并从科学工程applications.Topics的例子，如哈密顿系统的辛方法需要广泛的数学发展的实际和数学灵通的引进，介绍，有上进心，包括在演习，但一个完整的和严格的数学演示，而不是引用包括。这本书是适当的高年级本科生或开始与计算重点和执业工程师和科学家要了解计算差equations.A的数值分析的开始当然是需要的研究生，并在常微分方程的开始当然会有所帮助。

图书目录

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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