  The Maxey-Riley equations (MRE) describe the motion of a finite-sized,
spherical particle in a fluid. Because of wake effects, the force acting on a
particle depends on its past trajectory. This is modelled by an integral term
in the MRE, also called Basset force, that makes its numerical solution
challenging and memory intensive. A recent approach proposed by Prasath, Vasan
and Govindarajan exploits connections between the integral term and fractional
derivatives to reformulate the MRE as a time-dependent partial differential
equation on a semi-infinite pseudo-space. They also propose a numerical
algorithm based on polynomial expansions. This paper develops a numerical
approach based on finite difference instead, by adopting techniques by Koleva
and Fazio and Janelli to cope with the issues of having an unbounded spatial
domain. We compare convergence order and computational efficiency for particles
of varying size and density of the polynomial expansion by Prasath et al., our
finite difference schemes and a direct integrator for the MRE based on
multi-step methods proposed by Daitche.
