Our paper does not intend to compare the analytical and numerical models. Analytical model is used to find (estimate) the relevant non-dimensional form of the governing equations. We disagree with the reviewer comment that the stability analysis is incomplete. The stable and unstable regions are specified in our analysis. However, different unstable modes can grow and coexist below the critical limit and the fastest growing mode dominates the growth of instabilities and influence the shape of the resulting structures. Using numerical simulation, we have qualitatively shown the progress of physical instability for case 1 and 2 (Fig .7 and 8 in the paper). Nevertheless, the aim of this purpose is not to investigates different structure of instabilities. In fact, in our case, investigation of instabilities structure is not as easy as the reviewer suggests. Pure analytical methods, hold strong assumptions. Even if they give a reasonable prediction of the combustion front's speed and temperature, they may result in completely irrelevant stability criteria. In our formulation, although analytical methods used to define non-dimensional parameters, complete solution is achieved through numerical procedure. Thus, in our case, linear stability analysis, must be solved numerically. Instead, we have used numerical simulation to capture physical instabilities. Although, to date, numerical stability cannot be scrutinized, many physical instabilities are simulated using numerical procedures \cite{2001}. We have shown the convergence of the results in both spatial and temporal scale (Appendix 7.3). Also, we do not observe any spurious oscillation related to numerical instability in our simulation.