延時微分方程數值方法的穩(wěn)定性

內容概要

　　《延時微分方程數值方法的穩(wěn)定性》主要內容為常微分方程數值處理中的常用方法介紹；常復數線性延時微分方程數值方法如線性多步，Runge－Kutta方的P穩(wěn)定性、GP穩(wěn)定性、GPL－穩(wěn)定性，步長控制，步長與時間的矛盾；復系數延時微分方程的數值解及方法的穩(wěn)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(wěn)定性研究等等。

書籍目錄

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

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