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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.
‘The remarkable thing about this rule is that the error is of fourth order, as it is for Simpson's rule.’
‘Here is a program to compute the Simpson's rule approximation to an integral, along with some examples.’
‘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.’
‘We shall present new error inequalities for the modified Simpson's rule which quantify more precisely the error.’
‘Fixation probabilities to be used in Equation 10 were calculated by numerical integration using Simpson's rule.’
Origin
Late 19th century: named after Thomas Simpson (1710–61), English mathematician.