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A Simple "Filon-Trapezoidal" Rule

1967
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Mathematics of Computation
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Filon's quadrature is a formula for the approximate evaluation of Fourier integrals such as (1) F(o) = f dte^fit), J-T which retains uniform accuracy even when u is so large that many oscillations of the integrand occur within a given element oí of the range of integration. The original Filon formula [1] was derived on the assumption that/(f), rather than the complete integrand, may be approximated stepwise by parabolas, so that it may be called a 'Filon-Simpson' rule. More sophisticated

doi:10.2307/2004168
fatcat:f43ib5oxnndklh3d7ta4hw37v4