Revisiting neural-field calculation maps in the discrete case, we propose algorithmic mechanisms allowing to choose a right set of parameters in order to both (i) guaranty the stability of the calculation and (ii) tune the shape of the output map. These results do not ``prove'' the existence of stable bump solutions, this being already known and extensively verified numerically, but allow to calculate algorithmically the related parameters. The results apply to scalar and vectorial neural-fields thus allowing to bypass the inherent limitations brought by mean frequency models and also take the laminar structure of the cortex or high-level representation of cortical computations into account. We obtain an easy to implement procedure that guaranty the convergence of the map onto a fixed point, even with large sampling steps. Furthermore, we report how rectification is the minimal required non-linearity to obtain usual neural-field behaviors. We also propose a way to control and tune these behaviors (filtering, selection, tracking, remanence) and optimize the convergence rate. This applies to both non parametric profiles, i.e. adjusting the weight values directly, or to parametric profiles and thus adjusting their parameters (e.g. Mexican-hat profiles). Beyond these algorithmic results, the idea of studying neural computations as discrete dynamical systems and not only the discretization of a continuous system is emphasized here. The outcome is shared as an open-source plug-in module, called EnaS (http://enas.gforge.inria.fr), to be used in existing simulation software.