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On the stability of the linear delay differential and difference equations. (English) Zbl 1002.65098

The authors consider the initial-value problem for linear delay partial differential equations of parabolic type. A sufficient condition for the stability of this solution is presented. Stability estimates for the soluitons of difference schemes of the first- and second-order accuracy are given.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K45 Initial value problems for second-order parabolic systems
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