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Threshold stability of an improved IMEX numerical method based on conservation law for a nonlinear advection–diffusion Lotka–Volterra model

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  • Yang, Shiyuan
  • Liu, Xing
  • Zhang, Meng

Abstract

In this paper, we construct an improved Implicit–Explicit (IMEX) numerical scheme based on the conservation form of the advection–diffusion equations and study the numerical stability of the method in case of a nonlinear advection–diffusion Lotka–Volterra model. The classical numerical methods might be unsuitable for providing accurate numerical results for advection–diffusion problem in which advection dominates diffusion. An improved numerical scheme is proposed, which can preserve the positivity for arbitrary stepsizes. The convergence, boundedness, existence and uniqueness of the numerical solutions are investigated in paper. A threshold value denoted by R0Δx, is introduced in the stability analysis. It is shown that the numerical semi-trivial equilibrium is locally asymptotically stable if R0Δx<1 and unstable if R0Δx>1. Moreover, the limiting behaviors of the threshold value are exhibited. Finally, some numerical simulations are given to confirm the conclusions.

Suggested Citation

  • Yang, Shiyuan & Liu, Xing & Zhang, Meng, 2023. "Threshold stability of an improved IMEX numerical method based on conservation law for a nonlinear advection–diffusion Lotka–Volterra model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 127-144.
    • Handle: RePEc:eee:matcom:v:213:y:2023:i:c:p:127-144
    DOI: 10.1016/j.matcom.2023.06.009
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