Addition of these two terms will dominate the contribution to round-off error, which will be estimated in each time-step and solution will be update as follow.
where is the estimated round-off error calculated on the previous time-step (initially 0 ).
The performance of the ERKN64 is analyzed with round-off error control (WD) and without round-off error control (WO) technique applied to the Jovian problem.
Figure 4 explains the error growth in the angular momentum with and without round-off error control technique using the same tolerances and window size as for the set of experiments performed in Figure 2.
This indicates that the round-off error is the possible cause of these oscillations.
There are several methods to reduce the effects of round-off errors.
A very good reduction of round-off errors can be obtained by increasing the number of bits used for signal representation.
If reduction of round-off errors is desired, the number of bits used for the binary representation of [y.
The round-off errors (especially induced by limit-cycle) are more important when the filter approaches the steady-state and the outputs variations are small.
Influence of extra-precision bits over round-off errors Filter F1 (1:10) Filter F2 (1:20) [N.
However, for k = 6 and k = 7 we found the round-off error
to be so dominant (in the double-precision test runs) that the approximations produced by BOOTS were frequently inferior to the approximation from COLNEW.
16] (Table 2), hence the round-off errors become comparable with the results and propagate through the final result.
Propagation of the round-off errors through these two operations cause the method to fail, even though the absolute value of [(b/2).