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 Hölder norms for the solutions of the initial‐value problem of the delay differential and difference equations of the parabolic type.

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