A numerical method for solving reaction-advection-diffusion equations in irregular domains using the cellular automata

摘要

In this paper, a new numerical method is proposed to solve the reaction-advection-diffusion equation with spatio-temporal variation parameters by using the cellular automata. To this end, we first combine the finite difference method and the cellular automata to discretize the considered equation. The numerical solution and the corresponding convergence analysis are then carried out. A numerical simulation example is finally included to verify the feasibility and effectiveness of our proposed method.