Figure 4 shows the comparison results of angular acceleration's error calculated by the backward difference and the SGF.
As shown in Figure 4 and Table 5, the SGF provides about 28% more accurate angular acceleration than the results using the backward difference.
Backward Difference Formula (BDF) Runge-Kutta Method (RK4) and Differential Transform Method (DTM).
In order to see the comparison of the results with different numerical schemes the system of differential equations was solved using Runge-Kutta (RK4) and Backward Difference Formula (BDF).
Another possibility is to define it as the backward difference
Actually, in the discrete-time domain the single concept branches into two concepts, backward and forward Lie derivatives, depending on whether one applies in its definition the forward or backward difference (see formulae (9) and (10)).
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.
This defines the forward and backward difference operators
In , Wong established the following discrete Opial type inequality about the backward difference