Definition of Simpson's rule in English:

Simpson's rule


  • An arithmetical rule for estimating the area under a curve where the values of an odd number of ordinates, including those at each end, are known.

    • ‘We see that Simpson's rule has an error of much higher order in the small quantity h than the other rules, so that when M 4 is not too large, it is very advantageous for practical calculations.’
    • ‘Here is a program to compute the Simpson's rule approximation to an integral, along with some examples.’
    • ‘Fixation probabilities to be used in Equation 10 were calculated by numerical integration using Simpson's rule.’
    • ‘We shall present new error inequalities for the modified Simpson's rule which quantify more precisely the error.’
    • ‘The remarkable thing about this rule is that the error is of fourth order, as it is for Simpson's rule.’


Late 19th century: named after Thomas Simpson (1710–61), English mathematician.