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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 rate of change of the angle at time 3.4 using both the 2nd-order and 4th-order centred divided-difference formulae.
(1.35078 − 1.15775)/(2 ⋅ 0.1) = 0.96519 and (-1.44252 + 8⋅1.35078 − 8⋅1.15775 + 1.05837)/(12⋅0.1) = 0.96679.
Thus, 0.96679 is the more accurate answer, but even the 2nd-order formula is reasonably close. The data was taken from a curve which has an exact derivative of 0.96680 at 3.4.
Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.
