Asymptotic Stability of Runge-kutta Methods for the Pantograph Equations
نویسندگان
چکیده
This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay. ⎧⎨ ⎩ x′(t) +Bx(t) + Cx′(qt) +Dx(qt) = 0, t > 0, x(0) = x0, where B,C,D ∈ Cd×d, q ∈ (0, 1), and B is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a Lstable Runge-Kutta method can preserve the above-mentioned stability properties. Mathematics subject classification: 65L02, 65L05, 65L20.
منابع مشابه
Discretized Stability and Error Growth of The Nonautonomous Pantograph Equation
This paper is concerned with the stability properties of Runge–Kutta methods for the pantograph equation, a functional differential equation with a proportional delay. The focus is on nonautonomous equations. Both linear and nonlinear cases are considered. Sufficient and necessary conditions for the asymptotic stability of the numerical solution of general neutral pantograph equations are given...
متن کاملStability analysis of Runge–Kutta methods for nonlinear Volterra delay-integro-differential equations
This paper deals with the stability of Runge–Kutta methods for a class of stiff systems of nonlinear Volterra delay-integro-differential equations. Two classes of methods are considered: Runge–Kutta methods extended with a compound quadrature rule, and Runge– Kutta methods extended with a Pouzet type quadrature technique. Global and asymptotic stability criteria for both types of methods are de...
متن کاملAsymptotic Stability of Linear Delay Di erential Algebraic Equations and Numerical Methods
In this paper, we consider the asymptotic stability of linear constant coeecient delay diierential-algebraic equations and of-methods, Runge-Kutta methods and linear multistep methods applied to these systems.
متن کاملAsymptotic stability of linear delay differential-algebraic equations and numerical methods *
In this paper, we consider the asymptotic stability of linear constant coefficient delay differential-algebraic equations and of &methods, Runge-Kutta methods and linear multistep methods applied to these systems. o 1997 Published by Elsevier Science B.V.
متن کاملStability Analysis of Runge-Kutta Methods for Nonlinear Neutral Volterra Delay-Integro-Differential Equations
This paper is concerned with the numerical stability of implicit Runge-Kutta methods for nonlinear neutral Volterra delay-integro-differential equations with constant delay. Using a Halanay inequality generalized by Liz and Trofimchuk, we give two sufficient conditions for the stability of the true solution to this class of equations. Runge-Kutta methods with compound quadrature rule are consid...
متن کامل