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Positivity preserving finite volume scheme for the Nagumo-type equations on distorted meshes

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  • Zhou, Huifang
  • Sheng, Zhiqiang
  • Yuan, Guangwei

Abstract

In this paper we present a nonlinear positivity preserving finite volume scheme for the Nagumo-type equations with anisotropic tensor diffusion coefficient. For the diffusion term, we use the positivity preserving finite volume scheme. For the time direction, we use the backward Euler approximation. We deal with nonlinear reaction term implicitly and decompose nonlinear reaction coefficient into two nonnegative functions. Thus we get a system of nonlinear algebraic equations. The advantages of our scheme are that it can be applied to distorted meshes and has no severe constraint on the time step. The numerical results verify the theoretical result.

Suggested Citation

  • Zhou, Huifang & Sheng, Zhiqiang & Yuan, Guangwei, 2018. "Positivity preserving finite volume scheme for the Nagumo-type equations on distorted meshes," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 182-192.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:182-192
    DOI: 10.1016/j.amc.2018.04.058
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    References listed on IDEAS

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    1. Li, Xianping & Huang, Weizhang, 2017. "A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 49-67.
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