A remedy for the failure of the numerical steepest descent method on a class of oscillatory integrals (Q466798)

The author shows that the numerical method of steepest descent fails when applied in a straight forward fashion to the most commonly occuring highly oscillatory integrals. But through a polar change of variables, this oscillatory integral can be reformulated so that it can be solved efficiently using a combination of oscillatory integration and classical quadrature. The numerical experiments show that this approach avoids the failure in some cases.