An improved de-coupled solver of non-equilibrium flow was used to split the Euler equations for a reacting flow. Inviscid flux was calculated with fifth-order WENO scheme. Trapezoid formula and α-QSS methods were applied to deal with the stiffness generated by the chemical reacting source term of species equations separately. Time integration was performed with two-order TVD Runge-Kutta scheme. Cellular detonation of H₂/O₂/Ar in a straight tube was numerically studied. Calculated results by different methods were similar, and triple point structures were analyzed. The releasing heat of chemical reaction dealt with by α-QSSmethod is higher than that by trapezoid formula, so the detonation wave propagating speed of α-QSSmethod is higher than that of trapezoid formula too. Development of cellular structure was elaborated. Due to interactions between transverse waves and between transverse wave and tube wall, re-initiation was ignited, which plays a crucial role in the propagating of detonation wave. Ratio of numerical cellular structure length to width is consistent with reference value, which indicates the feasibility of the numerical method.