We investigate a selection of nominally first, second and fourth order time integration schemes with application to particle collision simulation using the discrete element method (DEM). The motivation being the typical requirement to efficiently two-way couple a continuum flow obtained with a finite volume solver employing an iterative implicit solution method to Lagrangian DEM. Using the linear force model to simulate particle repulsion, the actual order of accuracy with respect to initial separation ('free motion'), timestep, stiffness, damping and impact velocity is investigated. Due to the discontinuities of the inter-particle repulsive force upon contact, we find that without damping, the numerical schemes tested are generally limited to second order accuracy. The addition of damping can reduce actual order of accuracy further depending on the inter-particle free motion. This finding is compared against a continual interaction case (without free motion) where it is found that the expected higher order accuracy is recovered. Crown Copyright (C) 2009 Published by Elsevier Ltd. All rights reserved.