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The mathematical model describing transients in natural gas pipelines constitutes a non-homogeneous system of non-linear hyperbolic conservation laws. The energy equation is coupled to simulate the transient of temperature and acoustic wave speed in natural gas pipelines for the first time. The time splitting approach is adopted to solve this non-homogeneous hyperbolic model. At each time step, the non-homogeneous hyperbolic model is split into a homogeneous hyperbolic model and an ODE operator. An explicit 5-point, second-order-accurate total variation diminishing (TVD) scheme together with Lax-Wendroff (LW) scheme to treat the neighborhood nodes of boundary, is formulated to solve the homogeneous system of non-linear hyperbolic conservation laws. And apply the method of characteristics (MOC) to treat the boundary conditions at the inlet and the outlet of the pipeline. The pressure increased instantaneously at the inlet of pipeline and a real long pipeline's transients are used to test the efficacy of the hybrid schemes. The simulation results shown that the hybrid TVD/LW/MOC schemes can simulate real situation successfully of the physical variables in transient process.