منابع مشابه
Stability of the Discretized Pantograph Differential Equation
In this paper we study discretizations of the general pantograph equation y'(t) = ay(t) + by(6(t)) + cy'((t)), f>0, y(0)=y0, where a , b , c , and yo are complex numbers and where 9 and <¡> are strictly increasing functions on the nonnegative reals with 0(0) = <^>(0) = 0 and 8(t) < t, 4>(t) < t for positive /. Our purpose is an analysis of the stability of the numerical solution with trapezo...
متن کاملModeling of Pantograph-Catenary dynamic stability
The purpose of this paper is to describe the possibilities of studying the influence of forces external variables on the stability of motion of dynamical systems modeled by systems of differential equations with periodic coefficients of stability. The method is applied to analyze the influence of external harmonic forces on the stability of motion of the pantograph couple contact wire electric ...
متن کاملOn the asymptotic behavior of the pantograph equations
ẋ(t) = −a(t)x(t) + a(t)x(pt) , (1.1) where a(t) is a nonnegative continuous scalar function on R+ := [0 ,∞) and 0 < p < 1 is a constant. This equation is a special case of the so called pantograph equations arising in industrial applications [5,11]. The only solution of equation (1.1) with initial data x(0) = x0 is x(t) ≡ x0. However, if t0 > 0 and φ(t) is a given continuous function on [pt0 , ...
متن کاملDiscretized 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 کاملAsymptotic Stability of Runge-kutta Methods for the Pantograph Equations
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 co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the American Medical Association
سال: 1903
ISSN: 0002-9955
DOI: 10.1001/jama.1903.92490090015001f