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

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  • Zhang, Yanxia
  • Li, Xiaolin

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.

Suggested Citation

  • Zhang, Yanxia & Li, Xiaolin, 2026. "An element-free Galerkin method for linear and nonlinear delay-reaction-diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 707-723.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pb:p:707-723
    DOI: 10.1016/j.matcom.2025.11.003
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