微分方程数值方法引论_在线百科全书查询
微分方程数值方法引论
基本信息
作者：Mark H.Holmes
出版社: 科学出版社; 第1版 (2011年6月1日)
外文书名: Introduction to Numerical Methods in Differential Equations
丛书名: 国外数学名著系列(影印版)
精装: 238页
正文语种: 英语
开本: 16
ISBN: 9787030313874
条形码: 9787030313874
产品尺寸及重量: 24 x 17.4 x 1.8 cm ; 540 g
内容简介
本书内容包括：初值问题、两点边界值问题、扩散问题、平流方程、椭圆型问题等。
编辑推荐
霍姆斯编著的《微分方程数值方法引论（影印版）》是“国外数学名著系列”之一，内容包括：初值问题、两点边界值问题、扩散问题、平流方程、椭圆型问题等。可供高等院校数学系研究生、数学科研人员等学习参考。
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 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
