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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