Construction and analysis of some nonstandard finite difference methods for the FitzHugh-Nagumo equation
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| dc.contributor.author | Agbavon, Koffi Messan
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| dc.contributor.author | Appadu, A. Rao
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| dc.date.accessioned | 2021-02-08T06:22:51Z | |
| dc.date.issued | 2020-09 | |
| dc.description.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. | en_ZA |
| dc.description.department | Mathematics and Applied Mathematics | en_ZA |
| dc.description.embargo | 2021-04-30 | |
| dc.description.librarian | hj2021 | en_ZA |
| dc.description.uri | http://wileyonlinelibrary.com/journal/num | en_ZA |
| dc.identifier.citation | Agbavon KM, Appadu AR. Construction and analysis of some non-standard finite difference methods for the FitzHugh–Nagumo equation. Numerical Methods for Partial Differential Equations 2020;36:1145–1169. https://doi.org/10.1002/num.22468. | en_ZA |
| dc.identifier.issn | 0749-159X (print) | |
| dc.identifier.issn | 1098-2426 (online) | |
| dc.identifier.other | 10.1002/num.22468 | |
| dc.identifier.uri | http://hdl.handle.net/2263/78296 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | Wiley | en_ZA |
| dc.rights | © 2020 Wiley Periodicals, Inc., A Wiley Company. This is the pre-peer reviewed version of the following article : Construction and analysis of some non-standard finite difference methods for the FitzHugh–Nagumo equation. Numerical Methods for Partial Differential Equations 2020;36:1145–1169. https://doi.org/10.1002/num.22468. The definite version is available at : http://wileyonlinelibrary.com/journal/num. | en_ZA |
| dc.subject | Boundedness | en_ZA |
| dc.subject | Different regimes | en_ZA |
| dc.subject | Error estimates | en_ZA |
| dc.subject | FitzHugh–Nagumo equation | en_ZA |
| dc.subject | Nonstandard finite difference scheme | en_ZA |
| dc.subject | Positivity | en_ZA |
| dc.title | Construction and analysis of some nonstandard finite difference methods for the FitzHugh-Nagumo equation | en_ZA |
| dc.type | Postprint Article | en_ZA |
