(特价书)微分方程数值方法引论(英文影印版)

2.2Derivative Approximation Methods
2.2.1Matrix Problem
2.2.2Tridiagonal Matrices
2.2.3Matrix Problem Revisited
2.2.4Error Analysis
2.2.5Extensions
2.3Residual Methods
2.3.1Basis Functions
2.3.2Residual
2.4Shooting Methods
2.5Next Steps
Exercises
3Diffusion Problems
3.1Introduction
3.1.1Heat Equation
3.2Derivative Approximation Methods
3.2.1Implicit Method
3.2.2Theta Method
3.3Methods Obtained from Numerical Quadrature
3.3.1Crank-Nicolson Method
3.3.2L-Stability
3.4Methods of Lines
3.5Collocation
3.6Next Steps
Exercises
4Advection Equation
4.1Introduction
4.1.1Method of Characteristics
4.1.2Solution Properties
4.1.3Boundary Conditions
4.2First-Order Methods
4.2.1Upwind Scheme
4.2.2Downwind Scheme
4.2.3blumericul Domu'm of Dependence
4.2.4Stability
4.3Improvements
4.3.1Lax-Wendroff Method
4.3.2Monotone Methods
4.3.3Upwind Revisited
4.4 Implicit Methods
Exercises
5Numerical Wave Propagation
5.1Introduction
5.1.1Solution Methods
5.1.2Plane Wave Solutions
5.2Explicit Method
5.2.1Diagnostics
5.2.2Numerical Experiments
5.3Numerical Plane Waves
5.3.1Numerical Group Velocity
5.4Next Steps
Exercises
6Elliptic Problems
6.1Introduction
6.1.1Solutions
6.1.2Properties of the Solution
6.2Finite Difference Approximation
6.2.1Building the Matrix
6.2.2Positive Definite Matrices
6.3Descent Methods
6.3.1Steepest Descent Method
6.3.2Conjugate Gradient Method
6.4Numerical Solution of Laplace's Equation
6.5Preconditioned Conjugate Gradient Method
6.6Next Steps
Exercises
AAppendix
A.1 Order Symbols
A.2 Taylor's Theorem
A.3 Round-Off Error
A.3.1 Fhnction Evaluation
A.3.2 Numerical Differentiation
A.4 Floating-Point Numbers
References
Index