An element-free Galerkin method for linear and nonlinear delay-reaction-diffusion equations

Yanxia Zhang and Xiaolin Li

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PB, 707-723

Abstract: In this paper, an element-free Galerkin (EFG) method is proposed for solving delay-reaction–diffusion (DRD) equations. A fully discrete EFG system is developed by integrating a second-order time discretization with a penalized EFG spatial discretization. The unconditional stability of the time semi-discrete system is analyzed, and then the theoretical error of the meshless fully discrete system is derived. Finally, through numerical experiments, the validity of the method is verified and the theoretical result is confirmed.

Keywords: Delay-reaction–diffusion equation; Meshless methods; Element-free Galerkin method; Error analysis (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pb:p:707-723

DOI: 10.1016/j.matcom.2025.11.003

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