几何数值分析 第2版 英文

1 (p1): Ⅰ．Examples and Numerical Experiments
1 (p1-1): Ⅰ.1 First Problems and Methods
1 (p1-1-1): Ⅰ.1.1 The Lotka-Volterra Model
3 (p1-1-2): Ⅰ.1.2 First Numerical Methods
4 (p1-1-3): Ⅰ.1.3 The Pendulum as a Hamiltonian System
7 (p1-1-4): Ⅰ.1.4 The St？rmer-Verlet Scheme
8 (p1-2): Ⅰ.2 The Kepler Problem and the Outer Solar System
9 (p1-2-1): Ⅰ.2.1 Angular Momentum and Kepler's Second Law
10 (p1-2-2): Ⅰ.2.2 Exact Integration of the Kepler Problem
12 (p1-2-3): Ⅰ.2.3 Numerical Integration of the Kepler Problem
13 (p1-2-4): Ⅰ.2.4 The Outer Solar System
15 (p1-3): Ⅰ.3 The Hénon-Heiles Model
18 (p1-4): Ⅰ.4 Molecular Dynamics
21 (p1-5): Ⅰ.5 Highly Oscillatory Problems
21 (p1-5-1): Ⅰ.5.1 A Fermi-Pasta-Ulam Problem
23 (p1-5-2): Ⅰ.5.2 Application of Classical Integrators
24 (p1-6): Ⅰ.6 Exercises
27 (p2): Ⅱ．Numerical Integrators
27 (p2-1): Ⅱ.1 Runge-Kutta and Collocation Methods
28 (p2-1-1): Ⅱ.1.1 Runge-Kutta Methods
30 (p2-1-2): Ⅱ.1.2 Collocation Methods
34 (p2-1-3): Ⅱ.1.3 Gauss and Lobatto Collocation
35 (p2-1-4): Ⅱ.1.4 Discontinuous Collocation Methods
38 (p2-2): Ⅱ.2 Partitioned Runge-Kutta Methods
38 (p2-2-1): Ⅱ.2.1 Definition and First Examples
40 (p2-2-2): Ⅱ.2.2 Lobatto ⅢA-ⅢB Pairs
41 (p2-2-3): Ⅱ.2.3 Nystr？m Methods
42 (p2-3): Ⅱ.3 The Adjoint of a Method
43 (p2-4): Ⅱ.4 Composition Methods
47 (p2-5): Ⅱ.5 Splitting Methods
50 (p2-6): Ⅱ.6 Exercises
51 (p3): Ⅲ．Order Conditions,Trees and B-Series
51 (p3-1): Ⅲ.1 Runge-Kutta Order Conditions and B-Series
51 (p3-1-1): Ⅲ.1.1 Derivation of the Order Conditions
56 (p3-1-2): Ⅲ.1.2 B-Series
59 (p3-1-3): Ⅲ.1.3 Composition of Methods
61 (p3-1-4): Ⅲ.1.4 Composition of B-Series
64 (p3-1-5): Ⅲ.1.5 The Butcher Group
66 (p3-2): Ⅲ.2 Order Conditions for Partitioned Runge-Kutta Methods
66 (p3-2-1): Ⅲ.2.1 Bi-Coloured Trees and P-Series
68 (p3-2-2): Ⅲ.2.2 Order Conditions for Partitioned Runge-Kutta Methods
69 (p3-2-3): Ⅲ.2.3 OrderConditions for Nystr？m Methods
71 (p3-3): Ⅲ.3 Order Conditions for Composition Methods
71 (p3-3-1): Ⅲ.3.1…