A meshless collocation method with a global refinement strategy for reaction-diffusion systems on evolving domains

Abstract

Turing-type reaction-diffusion systems on evolving domains arising in biology, chemistry and physics are considered in this paper. The evolving domain is transformed into a reference domain, on which we use a second order semi-implicit backward difference formula (SBDF2) for time integration and a meshless collocation method for space discretization. A global refinement strategy is proposed to reduce the computational cost. Numerical experiments are carried out for different evolving domains. The convergence behavior of the proposed algorithm and the effectiveness of the refinement strategy are verified numerically.