Simpson's rule (redirected from Simpson formula)

Simpson's rule [′sim·sənz ‚rül]

(mathematics)

Also known as parabolic rule.

A basic approximation formula for definite integrals which states that the integral of a real-valued function ƒ on an interval [a,b] is approximated byh[ƒ(a) + 4ƒ(g+h) + ƒ(b)]/3, whereh= (b-a)/2; this is the area under a parabola which coincides with the graph of ƒ at the abscissasa,a+h, andb.

A method of approximating a definite integral over an interval which is equivalent to dividing the interval into equal subintervals and applying the formula in the first definition to each subinterval.

(petroleum engineering)

A mathematical relationship for calculating the oil- or gas-bearing net-pay volume of a reservoir; uses the contour lines from a subsurface geological map of the reservoir, including gas-oil and gas-water contacts.