Recurrent nets for tribology solutions

The contemporary problems of numerical calculations ocurring in powertrain tribology and transport problems demand the more and more exactness for obtained results.Moreover in performed calculations very important is the convergence, stability and reliability of the gained numerical values. The main scientific topic of the presented paper concerns the method of the determination of the optimum net for numerical calculations of partial difference and recurrence equations. The abovementioned optimum difference and recurrence method is referring to the stability of obtained particular and general numerical solutions and assures the convergence process of obtained calculation values. The Unit Net Region (UNR) was assumed at first for Laplace Operator. The optimum of the nod geometry localization was examined at first for UNR. The optimization index is defined and derived for UNR to determine the most useful net among the various geometries of the nods localization during the difference methods performances of partial recurrence numerical calculations. In the next considerations had been proved the corollary, where taking into account the optimum UNR, we can create optimum nets for other numerous partial difference and recurrence equations in discrete spaces. For example the numerous calculation results of presented optimum net for recurrent calculations are applied for numerical solutions of a Reynolds partial recurrence equation with variable coefficients in curvilinear orthogonal coordinates for curvilinear boundary conditions, and for other numerical problems occurring in applied and hydrodynamics.