This numerical integration method is an open Newton-Cotes formula; for each integral slice, Milne's rule samples three interior points (not the endpoints!) and combines them into an area estimate for this slice using the following formula:
Loading...Given a window of Loading... and a "step size" of Loading.... The point Loading... is the point Loading... steps into the window.
There is a simpler way to understand this! Milne's method is, in fact, just the midpoint method (see midpoint.cljc
), subject to a single refinement of "Richardson extrapolation".
The test namespace contains a symbolic proof that the Richardson-extrapolated Midpoint method is equivalent to using the formula above to calculate Milne's rule directly.