  Performing highly accurate simulations of droplet systems is a challenging
problem. This is primarily due to the interface dynamics which is complicated
further by the addition of surfactants. This paper presents a boundary integral
method for computing the evolution of surfactant-covered droplets in 2D Stokes
flow. The method has spectral accuracy in space and the adaptive time-stepping
scheme allows for control of the temporal errors. Previously available
semi-analytical solutions (based on conformal-mapping techniques) are extended
to include surfactants, and a set of algorithms is introduced to detail their
evaluation. These semi-analytical solutions are used to validate and assess the
accuracy of the boundary integral method, and it is demonstrated that the
presented method maintains its high accuracy even when droplets are in close
proximity.
