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

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