difference equation
Noun
Meaning
(mathematics) An equation involving an ordered sequence of real numbers (
{
a
n
}
n
=
1
∞
{\displaystyle \left\{a_{n}\right\}_{n=1}^{\infty }}
) and some of its differences, where the first difference is defined as
Δ
(
a
n
)
=
a
n
+
1
−
a
n
{\displaystyle \Delta (a_{n})=a_{n+1}-a_{n}\,}
and the k difference is defined recursively as
Δ
k
(
a
n
)
=
Δ
k
−
1
(
a
n
+
1
)
−
Δ
k
−
1
(
a
n
)
{\displaystyle \Delta ^{k}(a_{n})=\Delta ^{k-1}(a_{n+1})-\Delta ^{k-1}(a_{n})\,}
.
(mathematics) more broadly, any recurrence relation
Source: en.wiktionary.orgExamples
This results in : The difference equation (using the Direct Form I ) is : Frequency warping To determine the frequency response of a continuous-time filter, the transfer function is evaluated at which is on the axis.
For example, given a difference equation, one would set and for and evaluate.
In 1800, less than two years after his entry, he published two memoirs, one on Étienne Bézout 's method of elimination, the other on the number of integrals of a finite difference equation.
This nonlinear difference equation is intended to capture two effects: * reproduction where the population will increase at a rate proportional to the current population when the population size is small.