A combined Filon/asymptotic quadrature method for highly oscillatory problems (Q960019)

A special combination of an asymptotic expansion approach and Filon-type methods is employed for highly oscillatory integrals. It is known, that the usage of the traditional methods for oscillation yield schemes whose complexity grows with the oscillations' frequency. Theoretical analysis and numerical experiments demonstrate that the developed approach outperforms the conventional Filon-type method in many practical cases. It is shown that considerable savings in terms of the required number of potentially expensive moments can be expected. A generalization to the multivariate case is discussed briefly.