Construction and analysis of some nonstandard finite difference methods for the FitzHugh-Nagumo equation

dc.contributor.authorAgbavon, Koffi Messan
dc.contributor.authorAppadu, A. Rao
dc.date.accessioned2021-02-08T06:22:51Z
dc.date.issued2020-09
dc.description.abstractIn 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.departmentMathematics and Applied Mathematicsen_ZA
dc.description.embargo2021-04-30
dc.description.librarianhj2021en_ZA
dc.description.urihttp://wileyonlinelibrary.com/journal/numen_ZA
dc.identifier.citationAgbavon 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.issn0749-159X (print)
dc.identifier.issn1098-2426 (online)
dc.identifier.other10.1002/num.22468
dc.identifier.urihttp://hdl.handle.net/2263/78296
dc.language.isoenen_ZA
dc.publisherWileyen_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.subjectBoundednessen_ZA
dc.subjectDifferent regimesen_ZA
dc.subjectError estimatesen_ZA
dc.subjectFitzHugh–Nagumo equationen_ZA
dc.subjectNonstandard finite difference schemeen_ZA
dc.subjectPositivityen_ZA
dc.titleConstruction and analysis of some nonstandard finite difference methods for the FitzHugh-Nagumo equationen_ZA
dc.typePostprint Articleen_ZA

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