Positive and bounded nonstandard finite difference scheme for the Hodgkin-Huxley equations

DOI10.1007/s13160-018-0302-3zbMath1407.65089OpenAlexW2802398023MaRDI QIDQ1756732

Adebayo A. Aderogba, Michael Chapwanya

Publication date: 21 December 2018

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-018-0302-3

zbMATH Keywords

explicit schemesHodgkin-Huxley equationnon-standard finite difference

Mathematics Subject Classification ID

Neural biology (92C20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods for boundary value problems involving PDEs (65N06) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (3)

Robust septic Hermite collocation technique for singularly perturbed generalized Hodgkin–Huxley equation ⋮ Nonstandard finite difference approximation for a generalized fins problem ⋮ On the performance of some NSFD methods for a 2-D generalized Burgers–Huxley equation

Cites Work

• Unnamed Item
• Positive and elementary stable nonstandard numerical methods with applications to predator-prey models
• Nonstandard finite difference method by nonlocal approximation
• An unconditionally stable numerical method for the Luo-Rudy 1 model used in simulations of defibrillation
• A maximum principle for an explicit finite difference scheme approximating the Hodgkin-Huxley model
• Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences
• Exponential Time Differencing for Hodgkin--Huxley-like ODEs
• Topological dynamic consistency of non-standard finite difference schemes for dynamical systems
• An explicit nonstandard finite difference scheme for the Allen–Cahn equation
• The Backward Euler Method for Numerical Solution of the Hodgkin–Huxley Equations of Nerve Conduction
• An initial-boundary value problem of physiological significance for equations of nerve conduction
• Solving singularly perturbed advection–reaction equations via non‐standard finite difference methods

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