Methods for the discretisation of a simplified version of theConservation equation conservation equation, when only the convectiveConvective term and diffusive termsDiffusive term are considered, are described. The difficulty of this problem lies in the need to specify the variables at the interface between cells, which requires an application of interpolationInterpolation. The applicability of these methods is shown to depend on the values of thePeclet number Peclet number (P). For a one-dimensional problem, the central differencingCentral differencing approach (the value of a variable at the interface is assumed to be equal to the arithmetic average of its values in the centres of neighbouring cells) is shown to be applicable for small P, while the upwindUpwind approach (the value of a variable at the interface is assumed to be equal to the one in the centre of the upwind cell)Upwind is shown to be applicable for large P. These conclusions were inferred from a comparison of the predictions of these approaches and those of the analytical solution to aConvection-diffusion convection-diffusion equation. A discretisation based on this solution leads to an exponential approach. For small P, the latter reduces to the central differencingCentral differencing approach, while for large P it leads to the upwindUpwind approach.