《微分方程數值方法引論》是2011年科學出版社出版的圖書，作者是MarkH.Holmes。本書內容包括初值問題、兩點邊界值問題、擴散問題、平流方程、橢圓型問題等方面。
基本介紹
- 書名：微分方程數值方法引論
- 作者：Mark H.Holmes
- ISBN：9787030313874
- 頁數：238頁
- 出版社： 科學出版社
- 出版時間：(2011年6月1日
- 裝幀：精裝
- 開本：16
內容簡介,編輯推薦,目錄,
內容簡介
本書內容包括：初值問題、兩點邊界值問題、擴散問題、平流方程、橢圓型問題等。
編輯推薦
霍姆斯編著的《微分方程數值方法引論（影印版）》是“國外數學名著系列”之一，可供高等院校數學系研究生、數學科研人員等學習參考。
目錄
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 on a Wire
2.1.2 Chemical Kinetics
2.2 Derivative Approximation Methods
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 Diffusion Problems
3.1 Introduction
3.1.1 Heat Equation
3.2 Derivative Approximation Methods
3.2.1 Implicit Method
3.2.2 Theta Method
3.3 Methods Obtained from Numerical Quadrature
3.3.1 Crank-Nicolson Method
3.3.2 L-Stability
3.4 Methods of Lines
3.5 Collocation
3.6 Next Steps
Exercises
4 Advection Equation
4.1 Introduction
4.1.1 Method of Characteristics
4.1.2 Solution Properties
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 Solution Methods
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 Solution of 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 Fhnction Evaluation
A.3.2 Numerical Differentiation
A.4 Floating-Point Numbers
References
Index
