Abstract
The well-posedness of difference schemes of the initial value problem for delay differential equations with unbounded operators acting on delay terms in an arbitrary Banach space is studied. Theorems on the well-posedness of these difference schemes in fractional spaces are proved. In practice, the coercive stability estimates in Holder norms for the solutions of difference schemes of the mixed problems for delay parabolic equations are obtained.
Highlights
Approximate solutions of the delay differential equations have been studied extensively in a series of works and developed over the last three decades
It is difficult to generalize any numerical method to obtain a high order of accuracy algorithms, because high-order methods may not lead to efficient results
4 Conclusion In the present paper, the well-posedness of the difference schemes for the approximate solutions of the initial value problem for delay parabolic equations with unbounded operators acting on delay terms in an arbitrary Banach space is established
Summary
Approximate solutions of the delay differential equations have been studied extensively in a series of works (see, for example, [ – ] and the references therein) and developed over the last three decades. In Section , the coercive stability estimates in Hölder norms for the solutions of difference schemes for the approximate solutions of delay parabolic equations are obtained. For the solution of the difference scheme ( ) the coercive stability estimate in the norm of same fractional spaces Eα ( < α < ) under the supplementary restriction of the operator A is established.
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