Delay Differential Equations Definition/Meaning:
Ordinary differential equations where the
derivatives depend on values of the solution at the current value and several
previous values of the independent variable. The simplest form is
y(x) = ƒ(x, y(x), y(x - γ (x))), a ≤x ≤ b
where γ(x)≥0. To determine a solution, y(x)
must be specified on an interval a
≤x ≤ a where a depends on the values taken by
γ(x),
Most of the commonly used step-by-step methods for ordinary differential
equations can be adapted to problems of this form, although they have not yet
been developed to the same extent. It is necessary to incorporate an
interpolation scheme to approximate
(x -
γ(x))
to a value that will not usually coincide with a previously computed
approximation.
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