Dynamical technical networks and dynamic network objects (DNO) as a special case of them are considered in many subject areas as objects of research, design, quality assurance, automatization, monitoring and control. In this paper we focus on the simulation of the mine air networks (MAN) as an example of dynamic network objects with distributed parameters. To improve the simulation process, we propose to use new type of numerical methods — block difference methods (BDM). Because of the especial numerical structure these methods promise a possibility to optimize the simulation process to the parallel computing architectures. We introduce the first experimental results with a sequential version of the BDM-solvers and make a conclusion about the advisability of further steps in the direction of parallelization.