MarsdenとTaylorのFourier積分公式について

Abstract

Marsden and Taylor derived a quadrature formula for a Fourier integral whose form is the correction of Discrete Fourier Coefficients by the difference of higher order derivatives of f(χ) at the end points. Polynomial splines are used so that the coefficients in this formula are chosen to make the error vanish if f(χ) is a spline of degree κ. This formula is a good one, but the coefficients required in a actual computation are not yet given in a convenient form. To prevent the numerical instability in this formula, we derived another form of coefficients in this article. Numerical examples show the usefullness of this formula.