University of Cambridge 2004-08-19 KG.01 In this talk I will review recent advances, joint with Syvert Nřrsett, in understanding and implementing methods for quadrature with highly oscillatory kernels. We develop two methods, one based on an asymptotic expansion and the other on interpolation, that afford very precise approximation in the presence of high oscillation and critical points, in one or more dimensions.
Time allowing, I will describe some of the applications of these methods to Fredholm equations of the second kind and ordinary and partial differential equations with rapidly oscillating solutions. |
