On convolution quadrature and Hille-Phillips operational calculus

Abstract For the numerical approximation of convolution integrals and integral equations, quadrature methods are considered whose weights are constructed with the help of the Laplace transform of the convolution kernel and a linear multistep method. Convergence estimates are derived using the Hille-Phillips operational calculus and results of Brenner, Thomee and Wahlbin on difference methods for advection equations. A numerical application is given to a Schrodinger equation with short-range, time-dependent potential which is solved in a reformulation as a Volterra integral equation with singular, highly oscillatory kernel.