目录
- Preface
Chapter 1 Linear Multistep Methods
1．1 IntrodllCtion
1．2 Consistency，Convergence and Stability
1．3 The Highest Attainable Order
1．4 A一Stabilitv
Chapter 2 Runge-Kutta Methods
2．1 Order Condition
2．2 Numerical Stability 0f Explicit RK Methods
2．3 Numerical Stability of Implicit RK Methods
2．4 Multistep Runge-Kutta Methods
2．5 Suitabilitv and D-Suitabilitv of IRK Methods
Chapter 3 BDF Methods and Block Methods
3．1 IntrodUCtion
3．2 BDF Method 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 B10ck Methods with High Order Derivative
3．7 Block一Methods
Chapter 4 StabiHty ofMethods for Linear DDEs
4．1 Introduction
4．2 GP-Stability of一Methods
4．3 GPm-Stability 0f Linear Multistep Methods
4．4 Asymptotic Stabmty 0f Runge-Kutta Methods。
4．5 p-Stability of B10ck一Methods
4．6 DDEs with Variable Coefficients
4．7 PL-Stabilitv 0f Numerical Methods
4．8 GPL-stabilitv of Implicit RK Methods
4．9 GPL-stabilitv 0f Rosenbrock Methods
4．10 Step8ize and Time Connict
4．11 Big Picture
Chapter 5 Linear Systems 0f 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 0f DDEs with Multiple Delays
5．5 Asymptotic Stability of Rosenbrock Methods
5．6 Big Picture
Chapter 6 NonUnear Delay DifierentiaLl Equations
6．1 Properties of Analytical Solutions
6．2 RⅣand GRN-stabilitv
6．3 Asymptotic Stability of一Methods
6．4 Nonautonomous Linear Systeros
6．5 GPN and GRN-stabilitv of RK Methods
6．6 Big Picture
Chapter 7 Neutral Delay DifierentiaLl Equations
7．1 One-Parameter Methods
7．2 Asymptotic Behaviour of Analytical Solutions
7．3 ⅣGP-Stabilitv of()ne-Parameter Methods
7．4 Numerical Stabilitv 0f IRK Methods
7．5 IRK Methods for Generalized Neutral Systems
7．6 ⅣGPG-Stability of Linear Multistep Methods
7．7 The NPL-Stabilitv of Numerical Methods-
7．8 Big Picture
Chapter 8 Delay Volterra Integral Equations
8．1 Reducible Quadratare Rule
8．2 Numerical Stability of the Quadrature Rule
8．3 Numerical Stability of一methods
8．4 Big Pictllre
Chapter 9 Equations with Variable Delays
9．1 Introduction
9．2 Numerical Stability 0f一methods
9．3 AGPm-stability 0f一methods
9．4 NOillinear Pantograph Equations
9．5 Big Picture
AppelldixA Systeros with Bolmded Delays
AppelldiB L．mear Systeros of DDEs
AppelldixC StabiUty
Bibliography
SuggestiOil f0r Further Reading
Index
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