In the paper there has been made an advantage of the non-classical operational calculus to determination of the response of the certain discrete time-systems. The Z-transform is often used to analysis of the stationary discrete time-systems. However, the use of the Z-transform to determination of the response especially of the non-stationary discrete time-systems is doubtful or may cause complications. This method leads to differential equations of n-th order of variable coefficients, whose solutions are very difficult or impossible. The non-classical operational calculus can be used to analysis both of the stationary and non-stationary discrete time-systems. The presented method with the use of the Heaviside operator soon leads to the target without unnecessary differential equations.

In this work, safety analysis at the railway level crossings is presented using advanced mathematical modelling. Resistivity of track subgrade panels is taken into account. The analysis does not refer to the assessment of the current regulations. Specific cases of generalized dynamic system are considered by introducing operations S=Δ, S=P defined in space C(N) of real sequences. In this model, generalized discrete exponential and trigonometric functions that reflect the oscillatory nature of the analysed quantities are used. The advantage of the analyzes is the avoidance of numerical errors. We show also the importance of the resistivity of track subgrade panels in safety at the level crossings. The safety at the level crossings can be increased through providing track subgrade panels with appropriate resistivity to minimize negative effect of stray currents. The results may be used to evaluate selected safety indicators as well as to predict safety levels and to determine the ways of improving safety.