《延時微分方程數值方法的穩定性》主要內容為常微分方程數值處理中的常用方法介紹；常複數線性延時微分方程數值方法如線性多步，Runge－Kutta方的P穩定性、GP穩定性、GPL－穩定性，步長控制，步長與時間的矛盾；復係數延時微分方程的數值解及方法的穩定性；非線性延時微分奉承的數值處理；中立型微分方程數值方法的穩定性研究等等。
基本介紹
- 書名：延時微分方程數值方法的穩定性
- 出版社：科學出版社
- 頁數：308頁
- 開本：16
- 品牌：科學出版社
- 作者：科學出版社
- 出版日期：2007年3月27日
- 語種：簡體中文
- ISBN：9787030163172, 7030163176
內容簡介,圖書目錄,
內容簡介
《延時微分方程數值方法的穩定性》由科學出版社出版。
圖書目錄
Preface
Chapter 1 Linear Multistep Methods
1.1 Introduction
1.2 Consistency，Convergence and Stability
1.3 The Highest Attainable Order
1.4 A-Stability
Chapter 2 Runge-Kutta Methods
2.1 Order Condition
2.2 Numerical Stability of Explicit RK Methods
2.3 Numerical Stability of Implicit RK Methods
2.4 Multistep Runge-Kutta Methods
2.5 Suitability and D-Suitability of IRK Methods
Chapter 3 BDF Methods and Block Methods
3.1 Introduction
3.2 BDF Methods and Its Modified Form
3.3 Nordsieck Expression of BDF Methods
3.4 Block Implicit One-Step Methods
3.5 Non-equidistant Block Methods
3.6 Block Methods with High Order Derivative
3.7 Block θ-Methods
Chapter 4 Stability of Methods for Linear DDEs
4.1 Introduction
4.2 GP-Stability of θ-Methods
4.3 GPm-Stability of Linear Multistep Methods
4.4 Asymptotic Stability of Runge-Kutta Methods
4.5 P.Stability of Block θ-Methods
4.6 DDEs with Variable Coefficients
4.7 PL-Stability of Numerical Methods
4.8 GPL-stability of Implicit RK Methods
4.9 GPL-stability of Rosenbrock Methods
4.10 Stepsize and Time Conflict
4.11 Big Picture
Chapter 5 Linear Systems of DDEs
5.1 A Sufficient Condition for Asymptotic Stability
5.2 A Sufficient and Necessary Condition
5.3 Linear Systems of DDEs with Multiple Delays
5.4 Advanced Analysis of DDEs with Multiple Delays
5.5 Asymptotic Stability of Rosenbrock Methods
5.6 Big Picture
Chapter 6 Nonlinear Delay Differential Equations
6.1 Properties of Analytical Solutions
6.2 RN and GRN-stability
6.3 Asymptotic Stability of θ-Methods
6.4 Nonautonomous Linear Systems
6.5 GPN and GRN-stability of RK Methods
6.6 Big Picture
Chapter 7 Neutral Delay Differential Equations
7.1 One-Parameter Methods
7.2 Asymptotic Behaviour of Analytical Solutions
7.3 NGP-Stability of One-Parameter Methods
7.4 Numerical Stability of IRK Methods
7.5 IRK Methods for Generalized Neutral Systems
7.6 NGPG-Stability of Linear Multistep Methods
7.7 The NPL-Stability of Numerical Methods
7.8 Big Picture
Chapter 8 Delay Volterra Integral Equations
8.1 Reducible Quadrature Rule
8.2 Numerical Stability of the Quadrature Rule
8.3 Numerical Stability of θ-methods
8.4 Big Picture
Chapter 9 Equations with Variable Delays
Appendix A Systems with Bounded Delays
Appendix B Linear Systems of DDEs
Appendix C Stabiligy
Bibliography
Suggestion for Further Reading
Index
Chapter 1 Linear Multistep Methods
1.1 Introduction
1.2 Consistency，Convergence and Stability
1.3 The Highest Attainable Order
1.4 A-Stability
Chapter 2 Runge-Kutta Methods
2.1 Order Condition
2.2 Numerical Stability of Explicit RK Methods
2.3 Numerical Stability of Implicit RK Methods
2.4 Multistep Runge-Kutta Methods
2.5 Suitability and D-Suitability of IRK Methods
Chapter 3 BDF Methods and Block Methods
3.1 Introduction
3.2 BDF Methods and Its Modified Form
3.3 Nordsieck Expression of BDF Methods
3.4 Block Implicit One-Step Methods
3.5 Non-equidistant Block Methods
3.6 Block Methods with High Order Derivative
3.7 Block θ-Methods
Chapter 4 Stability of Methods for Linear DDEs
4.1 Introduction
4.2 GP-Stability of θ-Methods
4.3 GPm-Stability of Linear Multistep Methods
4.4 Asymptotic Stability of Runge-Kutta Methods
4.5 P.Stability of Block θ-Methods
4.6 DDEs with Variable Coefficients
4.7 PL-Stability of Numerical Methods
4.8 GPL-stability of Implicit RK Methods
4.9 GPL-stability of Rosenbrock Methods
4.10 Stepsize and Time Conflict
4.11 Big Picture
Chapter 5 Linear Systems of DDEs
5.1 A Sufficient Condition for Asymptotic Stability
5.2 A Sufficient and Necessary Condition
5.3 Linear Systems of DDEs with Multiple Delays
5.4 Advanced Analysis of DDEs with Multiple Delays
5.5 Asymptotic Stability of Rosenbrock Methods
5.6 Big Picture
Chapter 6 Nonlinear Delay Differential Equations
6.1 Properties of Analytical Solutions
6.2 RN and GRN-stability
6.3 Asymptotic Stability of θ-Methods
6.4 Nonautonomous Linear Systems
6.5 GPN and GRN-stability of RK Methods
6.6 Big Picture
Chapter 7 Neutral Delay Differential Equations
7.1 One-Parameter Methods
7.2 Asymptotic Behaviour of Analytical Solutions
7.3 NGP-Stability of One-Parameter Methods
7.4 Numerical Stability of IRK Methods
7.5 IRK Methods for Generalized Neutral Systems
7.6 NGPG-Stability of Linear Multistep Methods
7.7 The NPL-Stability of Numerical Methods
7.8 Big Picture
Chapter 8 Delay Volterra Integral Equations
8.1 Reducible Quadrature Rule
8.2 Numerical Stability of the Quadrature Rule
8.3 Numerical Stability of θ-methods
8.4 Big Picture
Chapter 9 Equations with Variable Delays
Appendix A Systems with Bounded Delays
Appendix B Linear Systems of DDEs
Appendix C Stabiligy
Bibliography
Suggestion for Further Reading
Index
