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An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations.
- Source :
-
International Journal of Computer Mathematics . Oct2019, Vol. 96 Issue 10, p1993-2009. 17p. - Publication Year :
- 2019
-
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]
Details
- Language :
- English
- ISSN :
- 00207160
- Volume :
- 96
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- International Journal of Computer Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 137508106
- Full Text :
- https://doi.org/10.1080/00207160.2018.1546849