Modelling Extreme-Mass-Ratio Inspirals using Pseudospectral Methods
  We introduce a new time-domain method for computing the self-force acting on
a scalar particle in a Schwarzschild geometry. The principal feature of our
method consists in the division of the spatial domain into several subdomains
and locating the particle at the interface betweem two them. In this way, we
avoid the need of resolving a small length scale associated with the presence
of a particle in the computational domain and, at the same time, we avoid
numerical problems due to the low differentiability of solutions of equations
with point-like singular behaviour.
