Moment-free numerical approximation of highly oscillatory integrals with stationary points
نویسنده
چکیده
We present a method for the numerical quadrature of highly oscillatory integrals with stationary points. We begin with the derivation of a new asymptotic expansion, which has the property that the accuracy improves as the frequency of oscillations increases. This asymptotic expansion is closely related to the method of stationary phase, but presented in a way that allows the derivation of an alternate approximation method that has the same asymptotic behaviour, but with significantly greater accuracy. This approximation method does not require moments.
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