Solving ordinary differential equations. 常微分方程的解法 / V.I = 2nd ed.

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 Attractors

Chapter 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 Equations

Chapter 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 Equations
Appendix. Fortran Codes
Bibliography
Symbol Index
Subject Index