Journal
INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM-2018)
Volume 2116, Issue -, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.5114020
Keywords
FitzHugh-Nagumo equation; Nonstandard finite difference scheme; positivity; boundedness
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Funding
- DST/NRF SARChI Chair in Mathematical Models and Methods in Bioengineering and Biosciences [M3B2, 82770]
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The FitzHugh-Nagumo equation has various applications in the fields of flame propagation, logistic population growth, neurophysiology, autocatalytic chemical reaction and nuclear theory [1, 6]. In this work, we construct three versions of nonstandard finite difference schemes in order to solve the FitzHugh-Nagumo equation with specified initial and boundary conditions under three different regimes. Properties of the methods such as positivity and boundedness are studied. The performances of the three methods is compared by computing L-1, L-infinity errors and CPU time at given time, T = 1.0.
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