RESEARCH ARTICLE
Construction and analysis of some nonstandard finite difference methods for the FitzHugh–Nagumo equation
Koffi M.
Agbavon,
Appanah Rao Appadu,
Koffi M. Agbavon
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa
Search for more papers by this authorCorresponding Author
Appanah Rao Appadu
Department of Mathematics and Applied Mathematics, Nelson Mandela University, Port Elizabeth, South Africa
Correspondence
Appanah Rao Appadu, Department of Mathematics and Applied Mathematics, Nelson Mandela University, University Way Summerstrand, 6031, Port Elizabeth, South Africa.
Email: [email protected]
Search for more papers by this authorKoffi M.
Agbavon,
Appanah Rao Appadu,
Koffi M. Agbavon
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa
Search for more papers by this authorCorresponding Author
Appanah Rao Appadu
Department of Mathematics and Applied Mathematics, Nelson Mandela University, Port Elizabeth, South Africa
Correspondence
Appanah Rao Appadu, Department of Mathematics and Applied Mathematics, Nelson Mandela University, University Way Summerstrand, 6031, Port Elizabeth, South Africa.
Email: [email protected]
Search for more papers by this authorAbstract
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.
CONFLICT OF INTERESTS
None of the authors have competing interests in the manuscript.
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