Abstract: In this paper, we study an efficient finite difference method based on constructed mesh for a class of semilinear parabolic equation arising from combustion process. Due to the influence of exponential source term, the considered model may theoretically describe the rigid ignition process in combustion. To catch the blowup and almost complete blowup phenomena, we introduce a cut-off level constant in the indicator attached to source term, so that the blowup position and moment can be approximated with less effort. Finally, numerical simulations with various settings of parameters and initial conditions are given to illustrate the excellent performance of numerical scheme, as well as fruitful dynamics of the blowup-combustion model.

Key words: Semilinear parabolic equation;Finite difference method, Exponential source, Monotonicity; Cut-off level function