1. An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations.
- Author
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Chapwanya, M., Jejeniwa, O. A., Appadu, A. R., and Lubuma, J. M.-S.
- Subjects
LINEAR differential equations ,ORDINARY differential equations ,NONLINEAR differential equations ,PARTIAL differential equations ,FINITE differences ,EQUATIONS - Abstract
In 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. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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