Since it is not clear whether this alternative generalizes to mixed-order systems of BVODEs, and, in any event, the costs are the same as those of the previous approach employing the [[Phi].
Therefore, for any system of BVODEs of the form (1), this bootstrap approach can generate at least [w.
Now we will use (12) to characterize a class of BVODEs for which this bootstrap approach is guaranteed to generate O([h.
2k]) approximations if the mixed system of BVODEs does not satisfy (13).
when handling mixed-order BVODEs directly, at most k - mmin bootstrap steps are performed, but, when handling its equivalent first-order form, exactly k - 1 bootstrap steps are performed.
Finally, note that the above system of BVODEs has many equivalent mixed-order forms.
We will use these BVODEs to test BOOTS under these different mixed-order configurations.
Note that this system of BVODEs does not satisfy (13).
This seemingly poor performance of BOOTS is due to the fact that COLNEW computes its approximations to linear BVODEs much more efficiently than nonlinear BVODEs because no Newton iterations are required.