As [h.sub.i] [right arrow] 0, the truncation error
tends to zero, which shows that scheme is consistent.
The relative truncation error
is set to be [[epsilon].sub.t] = [10.sup.-3] for the [mathematical expression not reproducible] is used to define the relative error of the H-LU factorization, where [[parallel]x[parallel].sub.F] denotes the Frobenius norm and I is an identity matrix.
So, the local truncation error
for [y.sup.n+1] is O([h.sup.4]).
Now, we will discuss the local truncation error
of the nonstandard scheme (10).
We do not calculate the ROC of the TOMs and BVM8 because their errors are mainly due to round-off errors rather than to truncation errors
. Figure 2 shows the efficiency curves of these methods.
The LUT method will consume excessive memory resources to achieve high accuracy; otherwise, the output signal of the LUT will be affected by truncation errors
due to the limited data depth.
where the term O represents the order of the truncation error
. Similarly, the first numerical partial derivative with respect to [delta] (and all other variables constant) with a second-order truncation error
centered finite difference would be given by
1 that as the truncation error
bounds becomes tighter as the truncation level, N, increases.
To bound the local discretization errors [[member of].sub.n], we need the following truncation error
Because the obtained analytical expressions were in the form of infinite summation series, their respective truncation error
bounds are also calculated.
The adaptive estimation methods in [9-11] have been adopted to improve the truncation error
. Instead of exhaustive computing resource simulation methods in previous works [9-11], the QE of SPPC multipliers is analyzed and derived from a simpler statistical method.
Equations (50) and (51) show the local truncation error
of the numerical scheme (24) with respect to the PDE (4).