(untitled) (Journal of Mathematical Study, 2021)
In this paper, we consider the numerical solution of the flame front equation, which is one of the most fundamental equations for modeling combustion theory. A schema combining a finite difference approach in the time direction and a spectral method for the space discretization is proposed. We give a detailed analysis for the proposed schema by providing some stability and error estimates in a particular case. For the general case, although we are unable to provide a rigorous proof for the stability, some numerical experiments are carried out to verify the efficiency of the schema. Our numerical results show that the stable solution manifolds have a simple structure when β is small, while they become more complex as the bifurcation parameter β increases. At last numerical experiments were performed to support the claim the solution of flame front equation preserves the same structure as K-S equation.