A new, innovative algorithm for the simulation of a turbocharger turbine based on the method of characteristics is introduced. This algorithm makes it possible to consider the variable inlet and outlet pressures as well as the variable gas properties. The theory of the method of characteristics is derived for ideal and perfect gases - the physical properties of the gas do not change with a variation in temperature and composition. New equations for the simulation of the boundary element suitable for considering the variation in gas properties and the tracking of the gas concentration are therefore derived. The improved equations and the improved algorithm ensure a much better conservation of mass flux for only a slightly increased computational time.