We are excited to announce that the repository will soon undergo an upgrade, featuring a new look and feel along with several enhanced features to improve your experience. Please be on the lookout for further updates and announcements regarding the launch date. We appreciate your support and look forward to unveiling the improved platform soon.
dc.contributor.author | Chapwanya, Michael![]() |
|
dc.contributor.author | Jejeniwa, O.A.![]() |
|
dc.contributor.author | Appadu, A. Rao![]() |
|
dc.contributor.author | Lubuma, Jean M.-S.![]() |
|
dc.date.accessioned | 2019-01-10T06:43:16Z | |
dc.date.issued | 2019-10 | |
dc.description.abstract | In this work, we consider numerical solutions of the FitzHugh–Nagumo system of equations describing the propagation of electrical signals in nerve axons. The system consists of two coupled equations: a nonlinear partial differential equation and a linear ordinary differential equation. We begin with a review of the qualitative properties of the nonlinear space independent system of equations. The subequation approach is applied to derive dynamically consistent schemes for the submodels. This is followed by a consistent and systematic merging of the subschemes to give three explicit nonstandard finite difference schemes in the limit of fast extinction and slow recovery. A qualitative study of the schemes together with the error analysis is presented. Numerical simulations are given to support the theoretical results and verify the efficiency of the proposed schemes. | en_ZA |
dc.description.department | Mathematics and Applied Mathematics | en_ZA |
dc.description.embargo | 2019-11-19 | |
dc.description.librarian | hj2019 | en_ZA |
dc.description.uri | http://www.tandfonline.com/loi/gcom20 | en_ZA |
dc.identifier.citation | M. Chapwanya, O. A. Jejeniwa, A. R. Appadu & J. M.-S. Lubuma (2018): An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations, International Journal of Computer Mathematics, vol. 96, no. 10, pp. 1993-2009, DOI: 10.1080/00207160.2018.1546849. | en_ZA |
dc.identifier.issn | 0020-7160 (print) | |
dc.identifier.issn | 1029-0265 (online) | |
dc.identifier.other | 10.1080/00207160.2018.1546849 | |
dc.identifier.uri | http://hdl.handle.net/2263/68119 | |
dc.language.iso | en | en_ZA |
dc.publisher | Taylor and Francis | en_ZA |
dc.rights | © 2018 Informa UK Limited, trading as Taylor & Francis Group. This is an electronic version of an article published in International Journal of Computer Mathematics, vol. x, no. y, pp. z-zz, 2018. doi : . International Journal of Computer Mathematics is available online at: http://www.tandfonline.com/loi/gcom20. | en_ZA |
dc.subject | Nonstandard finite difference | en_ZA |
dc.subject | Equilibrium point | en_ZA |
dc.subject | Kinematic model | en_ZA |
dc.subject | FitzHugh–Nagumo (FH-N) | en_ZA |
dc.subject | Dielectric waveguides | |
dc.subject | Finite difference method | |
dc.subject | Kinematics | |
dc.subject | Ordinary differential equations | |
dc.subject | Partial differential equations | |
dc.subject | Independent systems | |
dc.subject | Linear ordinary differential equations | |
dc.subject | Nonlinear partial differential equations | |
dc.subject | Qualitative properties | |
dc.subject | Nonlinear equations | |
dc.title | An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations | en_ZA |
dc.type | Postprint Article | en_ZA |