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2025, Volume 10, Issue 1: 777-792. doi: 10.3934/math.2025036
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Research article

Numerical solutions of multi-term fractional reaction-diffusion equations

  • 1.
    Henan College of Industry and Information Technology, Jiaozuo, Henan 454000, China
  • 2.
    Henan Jiaozuo Normal College, Jiaozuo, Henan 454000, China
  • Received: 08 December 2024 Revised: 03 January 2025 Accepted: 07 January 2025 Published: 14 January 2025

  • MSC : 65M12, 65M06, 35S10

  • In this paper, we have proposed a numerical approach based on generalized alternating numerical fluxes to solve the multi-term fractional reaction-diffusion equation. This type of equation frequently arises in the mathematical modeling of ultra-slow diffusion phenomena observed in various physical problems. These phenomena are characterized by solutions that exhibit logarithmic decay as time $ t $ approaches infinity. For spatial discretization, we employed the discontinuous Galerkin method with generalized alternating numerical fluxes. Temporal discretization was handled using the finite difference method. To ensure the robustness of the proposed scheme, we rigorously established its unconditional stability through mathematical induction. Finally, we conducted a series of comprehensive numerical experiments to validate the accuracy and efficiency of the scheme, demonstrating its potential for practical applications.

    Citation: Leqiang Zou, Yanzi Zhang. Numerical solutions of multi-term fractional reaction-diffusion equations[J]. AIMS Mathematics, 2025, 10(1): 777-792. doi: 10.3934/math.2025036

    Related Papers:

  • In this paper, we have proposed a numerical approach based on generalized alternating numerical fluxes to solve the multi-term fractional reaction-diffusion equation. This type of equation frequently arises in the mathematical modeling of ultra-slow diffusion phenomena observed in various physical problems. These phenomena are characterized by solutions that exhibit logarithmic decay as time $ t $ approaches infinity. For spatial discretization, we employed the discontinuous Galerkin method with generalized alternating numerical fluxes. Temporal discretization was handled using the finite difference method. To ensure the robustness of the proposed scheme, we rigorously established its unconditional stability through mathematical induction. Finally, we conducted a series of comprehensive numerical experiments to validate the accuracy and efficiency of the scheme, demonstrating its potential for practical applications.



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