《常微分方程的解法2:剛性與微分代數問題(影印版)(第2版)》是關於剛性微分方程和微分代數系統(帶約束項的微分方程)的解法《常微分方程的解法2:剛性與微分代數問題(影印版)(第2版)》共分四章,第一章介紹剛性問題的單步和外插法,第二章講述剛性問題的多步方法和一般線性方法,第三章討論奇異擾動問題的處理,第四章論述微分代數方程及其在約束力學系統中的套用。《常微分方程的解法2:剛性與微分代數問題(影印版)(第2版)》每一章從介紹方法開始,依次討論實際套用、數值結果、階和精度的理論分析,線性和非線性穩定性、收斂性和漸近展開。剛性問題和微分代數問題來源於科學計算的各個方面(如物理、化學、生物、控制工程、電網分析及力學系統)。《常微分方程的解法2:剛性與微分代數問題(影印版)(第2版)》包含了這些方面的各種套用及電腦程式。
基本介紹
- 書名：常微分方程的解法2:剛性與微分代數問題
- 出版社：科學出版社
- 頁數：614頁
- ISBN：7030166817
- 作者：海爾
- 出版日期：2006年12月20日
- 開本：16
- 品牌：科學出版社
內容簡介,圖書目錄,
內容簡介
2003年，在澳大利亞的悉尼舉行的ICIAM會議上，《常微分方程的解法2:剛性與微分代數問題(影印版)(第2版)》作者 Ernst Hairer和Gerhard Wanner被授予Peter Henrici獎。
圖書目錄
Chapter IV. Stiff Problems--One-step Methods
IV.1 Examples of Stiff Equations
IV.2 Stability Analysis for Explicit RK Methoods
IV.3 Stability Function of Implicit RK-Methods
IV.4 Order Stars
IV.5 Construction of Implicit Runge-Kutta Methods
IV.6 Diagonally Implicit RK Methods
IV.7 Rosenbrock-Type Methods
IV.8 Implementation of Implicit Runge-Kutta Methods
IV.9 Extrapolation Methods
IV.10 Numerical Experiments
IV.11 Contractivity for Linear Problems
IV.12 B-Stability and Contractivity
IV.13 Positive Quadrature Formulas and B-Stable RK-Methods
IV.14 Existence and Uniqueness of IRK Solutions
IV.15 B-Convergence
Chapter V. Multistep Methods for Stiff Problems
V.1 Stability of Multistep Methods
V.2 "Nearly" A-Stable Multistep Methods
V.3 Generalized Multistep Methods
V.4 Order Stars on Riemann Surfaces
V.5 Experiments with Multistep Codes
V.6 One-Leg Methods and G-Stability
V.7 Convergence for Linear Problems
V.8 Convergence for Nonlinear Problems
V.9 Algebraic Stability of General Linear Methods
Chapter VI. Singular Perturbation Problems and Index 1 Problems
VI.1 Solving Index 1 Problems
VI.2 Multistep Methods
VI.3 Epsilon Expansions for Exact and RK Solutions
VI.4 Rosenbrock Methods
VI.5 Extrapolation Methods
VI.6 Quasilinear Problems
Chapter VII. Differential-Algebraic Equations of Higher Index
VII.1 The Index and Various Examples
VII.2 Index Reduction Methods
VII.3 Multistep Methods for Index 2 DAE
VII.4 Runge-Kutta Methods for Index 2 DAE
VII.5 Order Conditions for Index 2 DAE
VII.6 Half-Explicit Methods for Index 2 Systems
VII.7 Computation of Multibody Mechanisms
VII.8 Symplectic Methods for Constrained Hamiltonian Systems
Appendix. Fortran Codes
Bibliography
Symbol Index
Subject Index
IV.1 Examples of Stiff Equations
IV.2 Stability Analysis for Explicit RK Methoods
IV.3 Stability Function of Implicit RK-Methods
IV.4 Order Stars
IV.5 Construction of Implicit Runge-Kutta Methods
IV.6 Diagonally Implicit RK Methods
IV.7 Rosenbrock-Type Methods
IV.8 Implementation of Implicit Runge-Kutta Methods
IV.9 Extrapolation Methods
IV.10 Numerical Experiments
IV.11 Contractivity for Linear Problems
IV.12 B-Stability and Contractivity
IV.13 Positive Quadrature Formulas and B-Stable RK-Methods
IV.14 Existence and Uniqueness of IRK Solutions
IV.15 B-Convergence
Chapter V. Multistep Methods for Stiff Problems
V.1 Stability of Multistep Methods
V.2 "Nearly" A-Stable Multistep Methods
V.3 Generalized Multistep Methods
V.4 Order Stars on Riemann Surfaces
V.5 Experiments with Multistep Codes
V.6 One-Leg Methods and G-Stability
V.7 Convergence for Linear Problems
V.8 Convergence for Nonlinear Problems
V.9 Algebraic Stability of General Linear Methods
Chapter VI. Singular Perturbation Problems and Index 1 Problems
VI.1 Solving Index 1 Problems
VI.2 Multistep Methods
VI.3 Epsilon Expansions for Exact and RK Solutions
VI.4 Rosenbrock Methods
VI.5 Extrapolation Methods
VI.6 Quasilinear Problems
Chapter VII. Differential-Algebraic Equations of Higher Index
VII.1 The Index and Various Examples
VII.2 Index Reduction Methods
VII.3 Multistep Methods for Index 2 DAE
VII.4 Runge-Kutta Methods for Index 2 DAE
VII.5 Order Conditions for Index 2 DAE
VII.6 Half-Explicit Methods for Index 2 Systems
VII.7 Computation of Multibody Mechanisms
VII.8 Symplectic Methods for Constrained Hamiltonian Systems
Appendix. Fortran Codes
Bibliography
Symbol Index
Subject Index
