A Python toolbox for the numerical solution of the Maxey‐Riley equation

The Maxey‐Riley equation (MRE) models the motion of a finite‐sized, spherical particle in a fluid. It is a second‐order integro‐differential equation with a kernel with a singularity at initial time. Because solving the integral term is numerically challenging, it is often neglected despite its often non‐negligible impact. Recently, Prasath et al. showed that the MRE can be rewritten as a time‐dependent heat equation on a semi‐infinite domain with a nonlinear, Robin‐type boundary condition. This approach avoids the need to deal with the integral term. They also describe a numerical approach for solving the transformed MRE based on Fokas method. We provide a Python toolbox implementing their approach, verify it against some of their numerical examples and demonstrate its flexibility by computing the trajectory of a particle in a velocity field given by experimental data.