常微分方程的解法1
2006-12
科学出版社
海尔
548
647000
无
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。 本书包括非刚性问题在物理、化学、生物和天文中的应用，计算机程序及数值比较。 第二版中重写了某些章节，增加了新的内容。
作者：(瑞士)海尔 等
Chapter I. Classical Mathematical Theory I.1 Terminology I.2 The Oldest Differential Equations I.3 Elementary Integration Methods I.4 Linear Differential Equations I.5 Equations with Weak Singularities I.6 Systme of Equations I.7 A General Existence Theorem I.8 Existence Theory using Iteration Methods and Taylor Series I.9 Existence Theory for Systems of Equations I.10 Differential Inequalities I.11 Systems of Linear Differential Equations I.12 Systmes with Constant Coefficients I.13 Stability I.14 Derivatives with Respect ot Parameters and Initial Values I.15 boundary Value and Eigenvalue Problems I.16 Periodic Solutions, Limit Cycles, Strange AttractorsChapter II. Runge-Kutta and Extrapolation Methods II.1 The First Runge-Kutta Methods II.2 Order Conditions for Runge-Kutta Methods II.3 Error Estimation and Convergence for RK Methods II.4 Practical Error Estimation and Step Size Selection II.5 Explicit Runge-Kutta Methods of Higher Order II.6 Dense Output, Discontinuities, Derviatives II.7 Implicit Runge-Kutta Methods II.8 Asymptotic Expansion of the Golbal Error II.9 Extrapolation Methods II.10 Numerical Comparisons II.11 Parallel Methods II.12 Composition of B-Series II.13 Higher Derivative Methods II.14 Numerical Methods for Second Order Differential Equations II.15 P-Series for Partitioned Differential Equations II.16 Symplectic Integration Methods II.17 Delay Differential EquationsChapter III. Multistep Methods and General Linear Methods III.1 Classical Linear Multistep Formulas III.2 Local Error and Order Conditions III.3 Stability and the First Dahlquist Barrier III.4 Convergence of Multistep Methods III.5 Variable Step Size Multistep Muthods III.6 Nordisieck Methods III.7 Implementation and Numerical Comparisons III.8 General Linear Methods III.9 Asymptotic Expansion of the Global Error III.10 Multistep Methods for Second Order Differential EquationsAppendix. Fortran CodesBibliographySymbol IndexSubject Index
《常微分方程的解法1:非刚性问题(第2版)(影印版)》是国际知名专家写的很权威的书。
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非常微分方程的解法刚性问题写的非常好,很经典的一本书国外用的特别多
专注讨论各种类型方程的解法，细致全面，读起来回味结论有可靠感！
经典好书，送货速度也给力。
很好的书，就是有点看不太懂
Prof.Butcherrecommendmetoreadthisbook;it'sgreatlyuseful
老师推荐的，虽然是英文的，但还是慢慢看吧
内容现代化，从中看到我们和西方先进国家基础数学教育方面的差距，我想这也是我们科技水平的差距
看着很好，包装很好。
二位不愧是数学大家！书中常引其他著名数学家之语句，足见二位对数学发展掌握之熟练！单看书中所用符号及公式编号便知是设计精巧之作品！二位对数学所做贡献让人赞叹不已！国内若有学者称对本书已熟练无疑，足可称为数学家了。（个人浅见）
书本里面有几张是坏的，太不给力了。。。