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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.
‘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.’
‘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.’
‘The remarkable thing about this rule is that the error is of fourth order, as it is for Simpson's rule.’
Origin
Late 19th century: named after Thomas Simpson (1710–61), English mathematician.