Numerical Quadrature of Highly Oscillatory Integrals Using Derivatives

  title={Numerical Quadrature of Highly Oscillatory Integrals Using Derivatives},
  author={Sheehan Olver},
Numerical approximation of highly oscillatory functions is an area of research that has received considerable attention in recent years. Using asymptotic expansions as a point of departure, we derive Filon-type and Levin-type methods. These methods have the wonderful property that they improve with accuracy as the frequency of oscillations increases. A generalization of Levin-type methods to integrals over higher dimensional domains will also be presented. 

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