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In this paper, we develop a new meshless numerical procedure for simulating the combustion model. To that end, we employ a local meshless collocation method according to the moving Taylor polynomial (MTP) approximation. The space derivative is approximated by using the local approach and then the Crank–Nicolson algorithm is utilized to approximate the time derivative. The stability and convergence of the time-discrete formulation are discussed, analytically and numerically. The Broyden method is applied to solve this nonlinear system. Since the size of the physical domain is large, we employ the non-overlapping domain decomposition method (DDM) to obtain a faster numerical algorithm. The local meshless approaches are efficient numerical techniques to simulate models in the fluid flow. The obtained results show that the proposed numerical formulation has efficient results for solving this mathematical model. [ABSTRACT FROM AUTHOR]