A MESHLESS COLLOCATION METHOD with A GLOBAL REFINEMENT STRATEGY for REACTION-DIFFUSION SYSTEMS on EVOLVING DOMAINS

Siqing Li, Zhonghua Qiao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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.

Original languageEnglish
Pages (from-to)601-617
Number of pages17
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume27
Issue number1
DOIs
Publication statusPublished - Jan 2022

Keywords

  • Evolving domain
  • Global refinement
  • Meshless method
  • Pattern formation
  • Reaction-diffusion systems

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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