Abstract

We propose an efficient family of algorithms for the approximation of Volterra integral equations of convolution type arising in two different applications. The first application we consider is the approximation of the fractional integral and associated fractional differential equations. The second application is the resolution of Schrödinger equations with concentrated potentials, which admit a formulation as systems of integral equations. In both cases, we are able to derive fast implementations of Lubich's Convolution Quadrature with very much reduced memory requirements and very easy to implement. Our algorithms are based on special contour integral representations of the Convolution Quadrature weights, according to the application, and special quadratures to compute them. Numerical experiments showing the performance of our methods will be shown.
This is joint work with Lehel Banjai (Heriot-Watt University)