This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the nume...This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the numerical processes that satisfy an important asymptotic stability condition related to the class of test problems y′(t)=ay(t)+by(t-τ) with a,b∈C, Re(a)<-|b| and τ>0. We prove that the block θ method is GP stable if and only if the method is A stable for ordinary differential equations. Furthermore, it is proved that the P and GP stability are equivalent for the block θ method.展开更多
This paper deals with the numerical solution of initial value problems for pantograph differential equations with variable delays. We investigate the stability of one leg θ-methods in the numerical solution of these ...This paper deals with the numerical solution of initial value problems for pantograph differential equations with variable delays. We investigate the stability of one leg θ-methods in the numerical solution of these problems. Sufficient conditions for the asymptotic stability of θ-methods are given by Fourier analysis and Ergodic theory.展开更多
Deals with the asymptotic stability properties of θ methods for the pantograph equation and the linear delay differential algebraic equation with emphasis on the linear θ methods with variable stepsize schem...Deals with the asymptotic stability properties of θ methods for the pantograph equation and the linear delay differential algebraic equation with emphasis on the linear θ methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ>1/2, and studies further the one leg θ method for the linear delay differential algebraic equation and establishes the sufficient asymptotic ally differential algebraic stable condition θ=1.展开更多
给出了FMP的三I解的一般形式 ,证明了关于区间值模糊推理的单调性定理、下确界定理以及存在性定理 .在分析了规则后件相对于前件的敏感性的基础上提出了 p 敏感参数概念 ,从而定义了 p 综合距离与 ( p θ)相对激活度 .将关于区间值模糊...给出了FMP的三I解的一般形式 ,证明了关于区间值模糊推理的单调性定理、下确界定理以及存在性定理 .在分析了规则后件相对于前件的敏感性的基础上提出了 p 敏感参数概念 ,从而定义了 p 综合距离与 ( p θ)相对激活度 .将关于区间值模糊推理的FOOL方法细致化为 ( p θ)算法 。展开更多
文摘This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the numerical processes that satisfy an important asymptotic stability condition related to the class of test problems y′(t)=ay(t)+by(t-τ) with a,b∈C, Re(a)<-|b| and τ>0. We prove that the block θ method is GP stable if and only if the method is A stable for ordinary differential equations. Furthermore, it is proved that the P and GP stability are equivalent for the block θ method.
文摘This paper deals with the numerical solution of initial value problems for pantograph differential equations with variable delays. We investigate the stability of one leg θ-methods in the numerical solution of these problems. Sufficient conditions for the asymptotic stability of θ-methods are given by Fourier analysis and Ergodic theory.
文摘Deals with the asymptotic stability properties of θ methods for the pantograph equation and the linear delay differential algebraic equation with emphasis on the linear θ methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ>1/2, and studies further the one leg θ method for the linear delay differential algebraic equation and establishes the sufficient asymptotic ally differential algebraic stable condition θ=1.
