A good approximation is to place the point in the middle of a small interval of distance.
Calculate the slope at a point which is half way between the beginning and end points of that small interval.
For tunnel constructions requiring small interval time for blasting, traditional geotechnical data collection approaches such as hand-mapping and geologic compass are always lacking in efficiency and accuracy.
A typical accidental slowing down of a turbine presents a rotor stator contact that may be limited to a small interval of the whole simulation period.
On each small interval we use hermitian shape functions of degree 3 to approximate the unknown function which is the solution of the system under study.
It is established by means of the quadratic interpolation approximation using three points (tj−2,f(tj−2)),ftj−1,f(tj−1)) and (tj,f(tj)) for the integrand f(t) on each small interval [tj−1,tj] (j⩾2), while the linear interpolation approximation is applied on the first small interval [t0,t1].
Within a limited computational domain, a detonation wave tends to form under the initial conditions with a small interval between hotspots, a low initial temperature of the unburnt mixture and a large temperature inhomogeneity.
The method is based on replacement of the non-linear vector field by a set of linear ones, each valid over a short segment of the evolving trajectory or over sufficiently small interval of time.
For a central impact after the first separation, band can catch up with the projectile such that a contact-impact state is re-established when m is in the small interval neighbouring m = 1.
In particular, it was found that a small interval of low frequencies are needed to recover the main traits of the relaxation for the stretched (β ≤ 1) and squeezed (β > 1) instances.
One is that the intersection points of all curves fall in a small interval and the intersection of any two curves represents the same changing rate of the horizontal ordinate, resulting in the maximum difference.
