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

Huifang Zhou, Zhiqiang Sheng and Guangwei Yuan

Applied Mathematics and Computation, 2018, vol. 336, issue C, 182-192

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.

Keywords: Positivity; Finite volume; Nagumo equation; Distorted meshes (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:336:y:2018:i:c:p:182-192

DOI: 10.1016/j.amc.2018.04.058

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