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.

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Etymology

Origin of Simpson's rule

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

Example Sentences

Simpson’s rule approximates the definite integral by first approximating the original function using piecewise quadratic functions.

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

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

From Textbooks • Mar. 30, 2016

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

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

From Textbooks • Mar. 30, 2016