A. Ashyralyev, P. E. Sobolevskii, "On the stability of the linear delay differential and difference equations", Abstract and Applied Analysis, vol. 6, Article ID 535262, 31 pages, 2001. https://doi.org/10.1155/S1085337501000616
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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