Regenerative gas cycles, including the Stirling engine, are sealed machines using pistons within cylinders to transfer energy from a heat source to a colder reservoir using a gas as working substance. For the optimal design of these cycles, we need a detailed description of gas dynamic behavior. This contribution deals with the simulation of cylinder spaces without internal combustion (as we find for regenerative gas cycles). For the simulation, we suggested a symbolic mathematics-based strategy to describe the dynamic system behavior based on partial non-linear differential equations for the conserved quantity. The renunciation of numerical approximation gives the advantage that the underlying physical mechanisms are characterized by exact expressions and parameters. Using some assumptions, the dynamic behavior of the gas within the cylinder is already described by ordinary non-linear differential equations. Depending on the selected boundary conditions analytical solutions can be obtained for some cases. Finally, the developed solution is based on it and will be received as a series expansion. Additionally, for the simulation-based optimization of the processes it is possible to calculate directly the periodical-steady state of the system with the help of the symbolic solution. The simulation is suitable for fundamental theoretical investigations, as well as for the implementation in simulation software for different regenerative gas cycles.