The numerical accuracy of a selection of different time integration techniques used to solve particle motion is investigated using a normal collision employing the non-linear Hertzian contact force. The findings are compared against the linear force model where it has been found that the expected order of accuracy of higher-order integration schemes is not realised (Tuley et al., 2010). The proposed mechanism for this limitation has been cited as the errors in integration which occur across the force profile discontinuity. By investigating the characteristics of both the non-linear elastic and the non-linear damped Hertzian contact models, it has been found that higher orders of accuracy are recoverable and depends on the degree of the governing non-linear equation. The numerical errors of the linear and non-linear force models are however markedly different in character. (C) 2013 Elsevier Ltd. All rights reserved.