Moment-free numerical integration of highly oscillatory functions

  title={Moment-free numerical integration of highly oscillatory functions},
  author={Sheehan Olver},
The aim of this paper is to derive new methods for numerically approximating the integral of a highly oscillatory function. We begin with a review of the asymptotic and Filon-type methods developed by Iserles and Nørsett. Using a method developed by Levin as a point of departure, we construct a new method that utilizes the same information as the Filon-type method, and obtains the same asymptotic order, while not requiring the computation of moments. We also show that a special case of this… CONTINUE READING
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