国外数学名著系列：常微分方程的解法1（非刚性问题）（第2版）（影印版）

图书标准信息

• 作者 海尔 著
• 出版社 科学出版社
• 出版时间 2006-12
• 版次 1
• ISBN 9787030166807
• 定价 78.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 548页
• 字数 647千字

【内容简介】

　　本书主要论述非刚性常微分方程。第一章介绍自牛顿、莱布尼兹、欧拉和哈密尔顿以来经典理论的历史发展，极限环及奇异吸引子。第二章用现代观念阐述龙格库塔方法和外插法，并讨论稠密输出的连续方法、并行龙格库塔方法、哈密尔顿系统的特殊方法、二阶常微分方程和时滞方程。第三章从多步方法的古典理论开始，论述变步长方法和Nordsieck方法及一般线性方法的理论。

【目录】

ChapterI.ClassicalMathematicalTheory
I.1Terminology
I.2TheOldestDifferentialEquations
I.3ElementaryIntegrationMethods
I.4LinearDifferentialEquations
I.5EquationswithWeakSingularities
I.6SystmeofEquations
I.7AGeneralExistenceTheorem
I.8ExistenceTheoryusingIterationMethodsandTaylorSeries
I.9ExistenceTheoryforSystemsofEquations
I.10DifferentialInequalities
I.11SystemsofLinearDifferentialEquations
I.12SystmeswithConstantCoefficients
I.13Stability
I.14DerivativeswithRespectotParametersandInitialValues
I.15boundaryValueandEigenvalueProblems
I.16PeriodicSolutions，LimitCycles，StrangeAttractors

ChapterII.Runge-KuttaandExtrapolationMethods
II.1TheFirstRunge-KuttaMethods
II.2OrderConditionsforRunge-KuttaMethods
II.3ErrorEstimationandConvergenceforRKMethods
II.4PracticalErrorEstimationandStepSizeSelection
II.5ExplicitRunge-KuttaMethodsofHigherOrder
II.6DenseOutput，Discontinuities，Derviatives
II.7ImplicitRunge-KuttaMethods
II.8AsymptoticExpansionoftheGolbalError
II.9ExtrapolationMethods
II.10NumericalComparisons
II.11ParallelMethods
II.12CompositionofB-Series
II.13HigherDerivativeMethods
II.14NumericalMethodsforSecondOrderDifferentialEquations
II.15P-SeriesforPartitionedDifferentialEquations
II.16SymplecticIntegrationMethods
II.17DelayDifferentialEquations

ChapterIII.MultistepMethodsandGeneralLinearMethods
III.1ClassicalLinearMultistepFormulas
III.2LocalErrorandOrderConditions
III.3StabilityandtheFirstDahlquistBarrier
III.4ConvergenceofMultistepMethods
III.5VariableStepSizeMultistepMuthods
III.6NordisieckMethods
III.7ImplementationandNumericalComparisons
III.8GeneralLinearMethods
III.9AsymptoticExpansionoftheGlobalError
III.10MultistepMethodsforSecondOrderDifferentialEquations
Appendix.FortranCodes
Bibliography
SymbolIndex
SubjectIndex