Numerical approximation of vector-valued highly oscillatory integrals
We present a method for the efficient approximation of integrals with highly oscillatory vector-valued kernels, such as integrals involving Airy functions or Bessel functions. We construct a vector-valued version of the asymptotic expansion, which allows us to determine the asymptotic order of a Levin-type method. Levin-type methods are constructed using collocation, and choosing a basis based on the asymptotic expansion results in an approximation with significantly higher asymptotic order.
highly oscillatory integrals asymptotics quadrature