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Delay Differential Equation


A delay differential equation (also called a differential delay equation or difference-differential equation, although the latter term has a different meaning in the modern literature) is a special type of functional differential equation. Delay differential equations are similar to ordinary differential equations, but their evolution involves past values of the state variable. The solution of delay differential equations therefore requires knowledge of not only the current state, but also of the state a certain time previously.

Examples include the equations defining the Dickman function

 {rho(u)=1   for 0<=u<=1; urho^'(u)+rho(u-1)=0   for u>1
(1)

and the Buchstab function

 {uomega(u)=1   for 1<=u<=2; (uomega(u))^'=omega(u-1)   for u>2
(2)

(Panario 1998).


See also

Differential-Algebraic Equation, Differential Equation, Functional Differential Equation

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References

Hayes, A. "Delay-Differential Equations." http://library.wolfram.com/infocenter/MathSource/725/.Norbury, J. and Wilson, R. E. "Dynamics of Constrained Differential Delay Equations." J. Comput. Appl. Math> 125, 201-215, 2000.Panario, D. "Smallest Components in Combinatorial Structures." Feb. 16, 1998. http://algo.inria.fr/seminars/sem97-98/panario.pdf.

Referenced on Wolfram|Alpha

Delay Differential Equation

Cite this as:

Weisstein, Eric W. "Delay Differential Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DelayDifferentialEquation.html

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