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سند علمی

An Euler-Maclaurin-like summation formula for Simpson’s rule

S. K. Lucas, James Madison

چکیده

where n is even, h = (b − a)/n, xi = a + ih, and ξ ∈ (a, b). We usually derive (1) using Lagrange polynomials or making the formula exact for f(x) = 1, x, x. A standard exercise for a numerical analysis class is to use the composite Simpson’s rule to approximate an integral with n equal to successive powers of two, and verify that (as long as the fourth derivative of f is well behaved) the errors reduce by a factor of sixteen due to the h term. Recently I assigned this exercise with the integral ∫ 1

اسناد مشابه

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