To develop a multiscale adaptive reduced chemistry solver (MARCS) for computationally efficient modeling of a reactive flow, the Hybrid Multi-Timescale (HMTS) method and G-Scheme have been evaluated and compared for both homogeneous auto-ignition and 1-D premixed spherical propagating flame calculations with detailed chemical kinetics of hydrogen, methane, dimethyl ether, and n-heptane. It is demonstrated that the CPU time of HMTS and G-Scheme methods depends on the number of species of the kinetic mechanisms, respectively, linearly and to the third power. For ignition, the results show that the G-Scheme method is faster than HMTS method when the species number of the chemical mechanism is below 40. The CPU Time of G-Scheme increases dramatically when the number of species of the detailed mechanisms is increased due to the huge computation cost of matrix inversion and reaction mode decomposition. Specifically, the G-Scheme method is faster at the induction stage of ignition and the near-equilibrium condition after ignition due to the large integration time step determined by the method adaptively. The HMTS method is faster at near the ignition point and for a large kinetic mechanism due to the fast convergence at a small base time step. Therefore, the present results suggest that it is possible an MARCS for computationally efficient modeling of combustion by adaptively taking the advantages of the computation efficiency of the HMTS method and the G-Scheme in different local combustion regimes and reduced mechanism sizes and integrating with the co-related dynamic adaptive chemistry and transport method (CO-DACT).