微分方程数值方法引论 本书特色
This book shows how to derive，test and analyze numerical methods for solving differential equations，including both ordinary and partial differential equations.The objective is that students learto solve differential equations numerically and understand the mathematical and computational issues that arise whethis is done. Includes aextensive collectioof exercises，which develop both the analytical and computational aspects of the material. Iadditioto more tha100 illustrations，the book includes a large collectioof supplemental material： exercise sets，MATLAB computer codes for both student and instructor，lecture slides and movies.
微分方程数值方法引论 内容简介
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微分方程数值方法引论 目录
Preface
1 Initial Value Problems
1．1 Introduction
1．1．1 Examples of IVPs
1．2 Methods Obtained from Numerical Differentiation．
1．2．1 The Five Steps
1．2．2 Additional Difference Methods
1．3 Methods Obtained from Numerical Quadrature
1．4 Runge——Kutta Methods
1．5 Extensions and Ghost Points
1．6 Conservative Methods
1．6．1 Velocity Verlet
1．6．2 Symplectic Methods
1．7 Next Steps
Exercises
2 Two-Point Boundary Value Problems
2．1 Introduction
2．1．1 Birds oa Wire
2．1．2 Chemical Kinetics
2．2 Derivative ApproximatioMethods
2．2．1 Matrix Problem
2．2．2 Tridiagonal Matrices
2．2．3 Matrix Problem Revisited
2．2．4 Error Analysis
2．2．5 Extensions
2．3 Residual Methods
2．3．1 Basis Functions
2．3．2 Residual
2．4 Shooting Methods
2．5 Next Steps
Exercises
3 DiffusioProblems
3．1 Introduction
3．1．1 Heat Equation
3．2 Derivative ApproximatioMethods
3．2．1 Implicit Method
3．2．2 Theta Method
3．3 Methods Obtained from Numerical Quadrature
3．3．1 Crank-NicolsoMethod
3．3．2 L-Stability
3．4 Methods of Lines
3．5 Collocation
3．6 Next Steps
Exercises
4 AdvectioEquation
4．1 Introduction
4．1．1 Method of Characteristics
4．1．2 SolutioProperties
4．1．3 Boundary Conditions
4．2 First-Order Methods
4．2．1 Upwind Scheme
4．2．2 Downwind Scheme
4．2．3 blumericul Domu'm of Dependence
4．2．4 Stability
4．3 Improvements
4．3．1 Lax-Wendroff Method
4．3．2 Monotone Methods
4．3．3 Upwind Revisited
4．4 Implicit Methods
Exercises
5 Numerical Wave Propagation
5．1 Introduction
5．1．1 SolutioMethods
5．1．2 Plane Wave Solutions
5．2 Explicit Method
5．2．1 Diagnostics
5．2．2 Numerical Experiments
5．3 Numerical Plane Waves
5．3．1 Numerical Group Velocity
5．4 Next Steps
Exercises
6 Elliptic Problems
6．1 Introduction
6．1．1 Solutions
6．1．2 Properties of the Solution
6．2 Finite Difference Approximation
6．2．1 Building the Matrix
6．2．2 Positive Definite Matrices
6．3 Descent Methods
6．3．1 Steepest Descent Method
6．3．2 Conjugate Gradient Method
6．4 Numerical Solutioof Laplace's Equation
6．5 Preconditioned Conjugate Gradient Method
6．6 Next Steps
Exercises
A Appendix
A．1 Order Symbols
A．2 Taylor's Theorem
A．3 Round-Off Error
A．3．1 FhnctioEvaluation
A．3．2 Numerical Differentiation
A．4 Floating-Point Numbers
References
Index
