Simpson's rule

American  

noun

Mathematics.

1. a method for approximating the value of a definite integral by approximating, with parabolic arcs, the area under the curve defined by the integrand.

---

Etymology

Origin of Simpson's rule

1895–1900; named after Thomas Simpson (1710–61), English mathematician

Example Sentences

For the following exercises, approximate the integrals using the midpoint rule, trapezoidal rule, and Simpson’s rule using four subintervals, rounding to three decimals.

From Textbooks • Mar. 30, 2016

This bound indicates that the value obtained through Simpson’s rule is exact.

From Textbooks • Mar. 30, 2016

Figure 3.16 With Simpson’s rule, we approximate a definite integral by integrating a piecewise quadratic function.

From Textbooks • Mar. 30, 2016

To understand the formula that we obtain for Simpson’s rule, we begin by deriving a formula for this approximation over the first two subintervals.

From Textbooks • Mar. 30, 2016

Use Simpson’s rule with n = 6 subdivisions to estimate the length of the ellipse when a = 2 and e = 1/3.

From Textbooks • Mar. 30, 2016