延时微分方程数值方法的稳定性
2005-1
科学出版社
科学出版社
295
《延时微分方程数值方法的稳定性》主要内容为常微分方程数值处理中的常用方法介绍;常复数线性延时微分方程数值方法如线性多步,Runge-Kutta方的P稳定性、GP稳定性、GPL-稳定性,步长控制,步长与时间的矛盾;复系数延时微分方程的数值解及方法的稳定性;非线性延时微分奉承的数值处理;中立型微分方程数值方法的稳定性研究等等。
Preface Chapter 1 Linear Multistep Methods1.1 Introduction1.2 Consistency,Convergence and Stability1.3 The Highest Attainable Order1.4 A-StabilityChapter 2 Runge-Kutta Methods2.1 Order Condition2.2 Numerical Stability of Explicit RK Methods2.3 Numerical Stability of Implicit RK Methods2.4 Multistep Runge-Kutta Methods2.5 Suitability and D-Suitability of IRK MethodsChapter 3 BDF Methods and Block Methods3.1 Introduction3.2 BDF Methods and Its Modified Form3.3 Nordsieck Expression of BDF Methods3.4 Block Implicit One-Step Methods3.5 Non-equidistant Block Methods3.6 Block Methods with High Order Derivative3.7 Block θ-MethodsChapter 4 Stability of Methods for Linear DDEs4.1 Introduction4.2 GP-Stability of θ-Methods4.3 GPm-Stability of Linear Multistep Methods4.4 Asymptotic Stability of Runge-Kutta Methods4.5 P.Stability of Block θ-Methods4.6 DDEs with Variable Coefficients4.7 PL-Stability of Numerical Methods4.8 GPL-stability of Implicit RK Methods4.9 GPL-stability of Rosenbrock Methods4.10 Stepsize and Time Conflict4.11 Big PictureChapter 5 Linear Systems of DDEs5.1 A Sufficient Condition for Asymptotic Stability5.2 A Sufficient and Necessary Condition5.3 Linear Systems of DDEs with Multiple Delays5.4 Advanced Analysis of DDEs with Multiple Delays5.5 Asymptotic Stability of Rosenbrock Methods5.6 Big PictureChapter 6 Nonlinear Delay Differential Equations6.1 Properties of Analytical Solutions6.2 RN and GRN-stability6.3 Asymptotic Stability of θ-Methods6.4 Nonautonomous Linear Systems6.5 GPN and GRN-stability of RK Methods6.6 Big PictureChapter 7 Neutral Delay Differential Equations7.1 One-Parameter Methods7.2 Asymptotic Behaviour of Analytical Solutions7.3 NGP-Stability of One-Parameter Methods7.4 Numerical Stability of IRK Methods7.5 IRK Methods for Generalized Neutral Systems7.6 NGPG-Stability of Linear Multistep Methods7.7 The NPL-Stability of Numerical Methods7.8 Big PictureChapter 8 Delay Volterra Integral Equations8.1 Reducible Quadrature Rule8.2 Numerical Stability of the Quadrature Rule8.3 Numerical Stability of θ-methods8.4 Big PictureChapter 9 Equations with Variable DelaysAppendix A Systems with Bounded DelaysAppendix B Linear Systems of DDEsAppendix C StabiligyBibliographySuggestion for Further ReadingIndex
《延时微分方程数值方法的稳定性》由科学出版社出版。
"延时微分方程"的需求其實很大,但可供選擇的書實在太少,可能因為這題目實在是太難了。本書在選材方面尚可接受,但實在要認真去勘誤!!!因為有不只一條最後算式有錯誤,對於須要本書的結果去殖入問題時會做成很大麻煩,因此在實用性方面要大大減去分數。