Unconditionally positivity and boundedness preserving schemes for a FitzHugh–Nagumo equation

Qin, Wendi; Ding, Deqiong; Ding, Xiaohua

doi:10.1080/00207160.2014.975696

Cited by 5 publications

(4 citation statements)

References 27 publications

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“…The condition ( 39) is comparable with (30), which effectively requires the mesh to be acute. The conditions (39) and (38) implies that…”

Section: Implicit Methods (Im)mentioning

confidence: 99%

“…This approximation has been used by Qin et al [39] for a finite difference solution of Nagumo's equation (with D = I). The approximation gives rise tõ…”

Section: Heim IImentioning

confidence: 99%

“…Understanding the former will help with understanding the latter. The numerical solution of Nagumotype equations and corresponding models has been studied extensively in the past; e.g., see [1,7,11,12,20,22,26,30,34,39,41]. However, very little attention has so far been paid to the studies of preservation of solution nonnegativity and boundedness in the discretization of Nagumo-type equations.…”

Section: Introductionmentioning

confidence: 99%

“…However, very little attention has so far been paid to the studies of preservation of solution nonnegativity and boundedness in the discretization of Nagumo-type equations. The existing work includes [7,32,39,41] where only finite difference discretization and isotropic diffusion have been considered. On the other hand, preservation of solution nonnegativity and boundedness has important physical implications and has attracted considerable attention from researchers in the recent years [7,14,15,16,28,29,31,38,43,46,47].…”

Section: Introductionmentioning

confidence: 99%

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A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations

Huang

2017

Applied Mathematics and Computation

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Preservation of nonnengativity and boundedness in the finite element solution of Nagumotype equations with general anisotropic diffusion is studied. Linear finite elements and the backward Euler scheme are used for the spatial and temporal discretization, respectively. An explicit, an implicit, and two hybrid explicit-implicit treatments for the nonlinear reaction term are considered. Conditions for the mesh and the time step size are developed for the numerical solution to preserve nonnegativity and boundedness. The effects of lumping of the mass matrix and the reaction term are also discussed. The analysis shows that the nonlinear reaction term has significant effects on the conditions for both the mesh and the time step size. Numerical examples are given to demonstrate the theoretical findings.

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“…The condition ( 39) is comparable with (30), which effectively requires the mesh to be acute. The conditions (39) and (38) implies that…”

Section: Implicit Methods (Im)mentioning

confidence: 99%

“…This approximation has been used by Qin et al [39] for a finite difference solution of Nagumo's equation (with D = I). The approximation gives rise tõ…”

Section: Heim IImentioning

confidence: 99%