[图书简介]
《常微分方程的解法Ⅱ：刚性与微分代数问题(第二版)))是关于刚性微分方程和微分代数系统(带约束项的微分方程)的解法。全书共分四章，第一章介绍刚性问题的单步和外插法，第二章讲述刚性问题的多步方法和一般线性方法，第三章讨论奇异扰动问题的处理，第四章论述微分代数方程及其在约束力学系统中的应用。本书每一章从介绍方法开始，依次讨论实际应用、数值结果、阶和精度的理论分析，线性和非线性稳定性、收敛性和渐近展开。刚性问题和微分代数问题来源于科学计算的各个方面(如物理、化学、生物、控制工程、电网分析及力学系统)。本书包含了这些方面的各种应用及计算机程序。
2003年，在澳大利亚的悉尼举行的ICIAM会议上，本书作者 Ernst Hairer和Gerhard Wanner被授予Peter Henrici奖。
[图书目录]
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
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