《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。
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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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