# Example 1

Given the data points ..., 3.2, 3.3, 3.4, 3.5, 3.6, ... which measure the rotation of a satellite dish at points in time, with angles 1.05837 1.15775 1.25554 1.35078 1.44252, approximate the acceleration of the angle at time 3.4 using both the 2nd-order and 4th-order centred divided-difference formulae for the 2nd derivative.

(1.35078 − 2⋅1.25554 + 1.15775)/0.1^{2} = −0.255 and
(-1.44252 + 16⋅1.35078 − 30⋅1.25554 + 16⋅1.15775 − 1.05837)/(12⋅0.1^{2}) = −0.2550833333⋅⋅⋅.

Thus, −0.25508333333 is the more accurate answer, but even the 2nd-order formula is reasonably close.

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.