On the stability of the linear delay differential and difference equations

We consider the initial-value problem for linear delay partial differential equations of the parabolic type. We give a sufficient condition for the stability of the solution of this initial-value problem. We present the stability estimates for the solutions of the first and second order accuracy difference schemes for approximately solving this initial-value problem. We obtain the stability estimates in Holder norms for the solutions of the initial-value problem of the delay differential and difference equations of the parabolic type.