We consider two new methods for numerical solution of a complete system of partial differential equations describing the flow of a gas mixture in pipeline systems. The first method tracks Lagrangian particles as they move together with the flow of transported fluid. When implementing this method, the flow parameters are found by means of a difference scheme, and the distribution of mass fractions of components and enthalpy of matter along the pipeline, by analyzing the motion of the Lagrangian particles. If we ignore the processes of diffusion, these particles must preserve their composition. The energy equation without diffusion and heat conduction reduces to an ordinary differential equation. The method proposed is free of artificial viscosity, because, for example, when considering the equation of continuity of components, variations in their specific mass fractions at any point in space are related only to physically meaningful processes, namely, to the inflow of "new" particles (with "new" specific mass fractions of the components). The second method includes constructing spline functions along the space and time coordinates of the computational mesh subject 1764 Sergey N. Pryalov and Vadim E. Seleznev to the fulfillment of differential equations at its nodes. The use of splines of high orders of approximation improves the accuracy of modeling. In addition, the spline schemes are fully conservative, which implies the possibility of satisfying not only the major integral conservation laws, but also all kinds of physically meaningful consequences of the system (for example, the laws of conservation of kinetic energy, internal energy, enthalpy etc.). Thus, the spline schemes enable producing credible solutions on difference schemes with a coarse space step, which makes them suitable for high-accuracy real-time modeling of multi-component gas mixture transport processes in complex-geometry branched pipeline systems. The approach used in constructing the spline schemes can be extended to the case of numerical modeling of a system of continuum mechanics equations in two-and three-dimensional settings.