  We describe a numerical method for the solution of acoustic exterior
scattering problems based on the time-domain boundary integral representation
of the solution. As the spatial discretization of the resulting time-domain
boundary integral equation we use either the method of fundamental solutions
(MFS) or the Galerkin boundary element method (BEM). In time we apply either a
standard convolution quadrature (CQ) based on an A-stable linear multistep
method or a modified CQ scheme. It is well-known that the standard low-order CQ
schemes for hyperbolic problems suffer from strong dissipation and dispersion
properties. The modified scheme is designed to avoid these properties. We give
a careful description of the modified scheme and its implementation with
differences due to different spatial discretizations highlighted. Numerous
numerical experiments illustrate the effectiveness of the modified scheme and
dramatic improvement with errors up to two orders of magnitude smaller in
comparison with the standard scheme
