  The gravitational-wave signals emitted by Extreme-Mass-Ratio Inspirals will
be hidden in the instrumental LISA noise and the foreground noise produced by
galactic binaries in the LISA band. Then, we need accurate gravitational-wave
templates to extract these signals from the noise and obtain the relevant
physical parameters. This means that in the modeling of these systems we have
to take into account how the orbit of the stellar-mass compact object is
modified by the action of its own gravitational field. This effect can be
described as the action of a local force, the self-force. We present a
time-domain technique to compute the self-force for geodesic eccentric orbits
around a non-rotating massive black hole. To illustrate the method we have
applied it to a testbed model consisting of scalar charged particle orbiting a
non-dynamical black hole. A key feature of our method is that it does not
introduce a small scale associated with the stellar-mass compact object. This
is achieved by using a multidomain framework where the particle is located at
the interface between two subdomains. In this way, we just have to evolve
homogeneous wave-like equations with smooth solutions that have to be
communicated across the subdomain boundaries using appropriate junction
conditions. The numerical technique that we use to implement this scheme is the
pseudospectral collocation method. We show the suitability of this technique
for the modeling of Extreme-Mass-Ratio Inspirals and show that it can provide
accurate results for the self-force.
