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The study on neutral differential equations is more intricate than that on ordinary delay differential equations.
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Ordinary delays have been largely replaced by short-interval delays but are still used to a considerable extent for such purposes as driving tunnels and sinking shafts.
For the millions of commuters required to report today for their first workday of 2001, there was little expectation of any out-of-the-ordinary delays.
Bellen and Zennaro [11] gave the theoretical aspects of numerical methods for ordinary and delay differential equations, and suitable techniques for solving numerically such type of equations.
It is worthwhile mentioning that several important problems of the theory of ordinary and delay differential equations lead to investigations of functional differential equations of various types (see the books by Hale and Verduyn Lunel, Wu, and articles by Liang, Xiao, Mophou, N'Guérékata, Benchohra, Lizama, Hernandez, etc. and the references therein).
It is worthwhile mentioning that several important problems of the theory of ordinary and delay differential equations lead to investigations of functional differential equations of various types (see the books by Hale and Verduyn Lunel [1], Wu [2], Liang et al. [3], Liang and Xiao [4 9], and the references therein).
Up-to-date models were taken from the literature in the form of ordinary and delay differential equations.
But if that's now going to happen at railway stations and on ordinary streets, delaying and degrading us without even a holiday at the end of it, should we not have a little chat first?
The present method is believed to be applicable to any self-excited system having a large degree of instability that is not removable by an ordinary time-delayed feedback.
The benefits may be worth it: blockchains are secure, scalable, and versatile, and could conceivably replace legacy systems that limit or delay ordinary operations.
Some authors developed the Laguerre spectral method for the half line for ordinary, partial, and delay differential equations; see [21 25].
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