Discretized Stability and Error Growth of The Nonautonomous Pantograph Equation

University of Cambridge Exact and Discretized Stability of the Pantograph Equation Arieh Iserles Exact and Discretized Stability of the Pantograph Equation

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...

An efficient numerical method for singularly perturbed second order ordinary differential equation

In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...

On the Dynamic of a Nonautonomous

Nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential equations which model various diverse phenomena in biology, ecology, economics, physics and engineering. The study of dynamical properties of such equations is of great importance in many areas. The autonomous difference equat...

Asymptotic 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...