The discrete element method (DEM) is becoming widely used to simulate granular flows. This method simulates the individual dynamics of all particles in an assembly by numerically integrating their acceleration resulting from all the contact forces. It is generally recognised that such a complex model must be validated by comparison with experimental results. Indeed the authors have addressed this in earlier publications given in the references. However, one important aspect is often given little attention, and that is testing the code to ensure that the computer program executes the model specification correctly. This paper describes in detail a DEM program for cohesive particle vibration and shows some simple simulations that have helped to verify the code. It is concluded that these 'mathematical tests' on artificial situations can uncover bugs in programs that appear to be running correctly, even if they appear to simulate real experiments reasonably well. These tests are published with the aim of helping others validate their programs in similar applications. The paper also discusses the widely used simplification of particle-particle interactions by Hooke's law and suggests that its validity depends upon the application. The main limitation of the DEM technique is the computational (CPU) time required. Techniques to minimise this are described, in particular in relation to particle referencing and array sizes. The runtimes shown illustrate the importance of optimising array sizes for the neighbourhood lists.