# backward difference

## backward difference

[¦bak·wərd ′dif·rəns]
(mathematics)
One of a series of quantities obtained from a function whose values are known at a series of equally spaced points by repeatedly applying the backward difference operator to these values; used in interpolation and numerical calculation and integration of functions.
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The Grunwald-Letnikov variable-, fractional-order backward difference with step h >0 (GL-VFOBD-h) of function x(*) with an order function v: Z [right arrow] [R.sub.+] [union] {0} started at [k.sub.0] = 0 is defined as a finite sum
In the next definition, the Grunwald-Letnikov fractional-order backward difference (GL-FOBD) is generalized to the Grunwald-Letnikov variable-, fractional-order backward difference (GL-VFOBD) in part (a) and to the Grunwald-Letnikov variable-, fractional-order backward difference with initialization (GL-VFOBDwl) in part (b).
Figure 4 shows the comparison results of angular acceleration's error calculated by the backward difference and the SGF.
Backward Difference Formula (BDF) Runge-Kutta Method (RK4) and Differential Transform Method (DTM).
For the lower boundary, where i = M, substitute the approximate unknown value of the right boundary by the backward difference approximation to [partial derivative]C/[partial derivative]x = 0.
 have introduced onepoint backward difference methods for solving higher-order ODEs.
In this paper, we proposed a dynamic compensation method based on a digital filter with backward difference design.
where [DELTA] f (x) = f (x + 1) - f (x) and [nabla] (x) = f (x) - f (x - 1) denote the forward and backward difference operators, respectively.
In , Wong established the following discrete Opial type inequality about the backward difference operator:
For stabilization of the calculations the first equation of (2.1) is approximated by using backward differences formula:

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