Chapwanya, MichaelJejeniwa, O.A.Appadu, A. RaoLubuma, Jean M.-S.2019-01-102019-10M. Chapwanya, O. A. Jejeniwa, A. R. Appadu & J. M.-S. Lubuma (2018): An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations, International Journal of Computer Mathematics, vol. 96, no. 10, pp. 1993-2009, DOI: 10.1080/00207160.2018.1546849.0020-7160 (print)1029-0265 (online)10.1080/00207160.2018.1546849http://hdl.handle.net/2263/68119In this work, we consider numerical solutions of the FitzHugh–Nagumo system of equations describing the propagation of electrical signals in nerve axons. The system consists of two coupled equations: a nonlinear partial differential equation and a linear ordinary differential equation. We begin with a review of the qualitative properties of the nonlinear space independent system of equations. The subequation approach is applied to derive dynamically consistent schemes for the submodels. This is followed by a consistent and systematic merging of the subschemes to give three explicit nonstandard finite difference schemes in the limit of fast extinction and slow recovery. A qualitative study of the schemes together with the error analysis is presented. Numerical simulations are given to support the theoretical results and verify the efficiency of the proposed schemes.en© 2018 Informa UK Limited, trading as Taylor & Francis Group. This is an electronic version of an article published in International Journal of Computer Mathematics, vol. x, no. y, pp. z-zz, 2018. doi : . International Journal of Computer Mathematics is available online at: http://www.tandfonline.com/loi/gcom20.Nonstandard finite differenceEquilibrium pointKinematic modelFitzHugh–Nagumo (FH-N)Dielectric waveguidesFinite difference methodKinematicsOrdinary differential equationsPartial differential equationsIndependent systemsLinear ordinary differential equationsNonlinear partial differential equationsQualitative propertiesNonlinear equationsPostprint Article