Open AccessA meshless collocation method with a global refinement strategy for reaction-diffusion systems on evolving domains
Author(s) -
Siqing Li,
Zhonghua Qiao
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021057
Subject(s) - discretization , regularized meshless method , collocation (remote sensing) , domain (mathematical analysis) , reaction–diffusion system , computer science , convergence (economics) , mathematics , collocation method , diffusion , turing , algorithm , mathematical optimization , singular boundary method , mathematical analysis , finite element method , ordinary differential equation , differential equation , physics , machine learning , boundary element method , economics , thermodynamics , economic growth , programming language
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.