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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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    References listed on IDEAS

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    1. Tang, Changyang & Zhang, Chengjian, 2021. "A fully discrete θ-method for solving semi-linear reaction–diffusion equations with time-variable delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 48-56.
    2. Sun, Fengxin & Wang, Jufeng & Xu, Ying, 2024. "An improved stabilized element-free Galerkin method for solving steady Stokes flow problems," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    3. Omran, A.K. & Zaky, M.A. & Hendy, A.S. & Pimenov, V.G., 2022. "An easy to implement linearized numerical scheme for fractional reaction–diffusion equations with a prehistorical nonlinear source function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 218-239.
    4. Li, Xiaolin & Dong, Haiyun, 2025. "Analysis of a stabilized element-free Galerkin method for magnetohydrodynamic flow at very large Hartmann numbers," Applied Mathematics and Computation, Elsevier, vol. 495(C).
    5. Luo, Xu-Bao & Li, D.M. & Liu, Bin, 2023. "A comparison study of the efficiency and accuracy of IEFG in solving elasticity problems using different nodal integration schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 561-587.
    6. Zhao, Jingjun & Zhan, Rui & Xu, Yang, 2018. "D-convergence and conditional GDN-stability of exponential Runge–Kutta methods for semilinear delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 45-58.
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