The Influence of Interpolation on the Global Error in Retarded Differential Equations

Abstract

Consider the retarded initial value problem

$$\begin{gathered} y'(x) = f(x,y(x),y(x - \tau ))\quad for\quad x\underline > {x_o}, \hfill \\ y(x) = \psi (x)\quad \quad \quad \quad \quad \quad for\quad x\underline > {x_o}, \hfill \\ \end{gathered} $$

(1)

where the retardation τ may be constant, variable: τ = τ(x), or state dependent: τ = τ(x,y(x)), and τ ≥ o. If f, ψ and τ are continuous then according to DRIVER [2] there exists a solution of problem (1) in some interval [x_o,b].