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- Title
Construction and analysis of some nonstandard finite difference methods for the FitzHugh–Nagumo equation.
- Authors
Agbavon, Koffi M.; Appadu, Appanah Rao
- Abstract
In this work, we construct four versions of nonstandard finite difference schemes in order to solve the FitzHugh–Nagumo equation with specified initial and boundary conditions under three different regimes giving rise to three cases. The properties of the methods such as positivity and boundedness are studied. The numerical experiment chosen is quite challenging due to shock‐like profiles. The performance of the four methods is compared by computing L1, L∞ errors, rate of convergence with respect to time and central processing unit time at given time, T = 0.5. Error estimates have also been studied for the most efficient scheme.
- Subjects
FINITE difference method; NONSTANDARD mathematical analysis; CENTRAL processing units; EQUATIONS; UNITS of time
- Publication
Numerical Methods for Partial Differential Equations, 2020, Vol 36, Issue 5, p1145
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22468