Elaboration of an evolving calculation domain for the resolution of a fire spread model

In a previous study, we proposed a two-dimensional reaction-diffusion equation to model fire spread. Our objective is to generate a forest fire simulator. This led us to develop a resolution algorithm capable of reducing the calculation time. This algorithm, applied to the finite difference method, is described here. The solution is calculated for only a certain number of points of the study domain. The calculation domain is dynamically decreased or increased according to the evolution of the solution. The algorithm tested for the fire spread model can be used to solve all reaction-diffusion equations that possess a spreading solution.