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International Journal of Computer Mathematics Volume 96, 2019 - Issue 10
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Original Articles

An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations

M. ChapwanyaDepartment of Mathematics & Applied Mathematics, University of Pretoria, Pretoria, South AfricaCorrespondence[email protected]
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,
O. A. JejeniwaDepartment of Mathematics & Applied Mathematics, University of Pretoria, Pretoria, South AfricaView further author information
,
A. R. AppaduDepartment of Mathematics & Applied Mathematics, University of Pretoria, Pretoria, South AfricaView further author information
&
J. M.-S. LubumaDepartment of Mathematics & Applied Mathematics, University of Pretoria, Pretoria, South AfricaView further author information
Pages 1993-2009 | Received 13 May 2018, Accepted 04 Nov 2018, Published online: 19 Nov 2018

Citations (12)

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W. D. Qin, Z. Y. Man, X. H. Ding & S. Z. Lu. (2021) A class of nonstandard finite difference methods for the Burgers–Huxley equation. Journal of Difference Equations and Applications 27:9, pages 1373-1394.
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Amit Kumar Verma & Sheerin Kayenat. (2020) An efficient Mickens' type NSFD scheme for the generalized Burgers Huxley equation. Journal of Difference Equations and Applications 26:9-10, pages 1213-1246.
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Articles from other publishers (10)

Huanrong Li & Rushuang Yang. (2023) Analysis of two spectral Galerkin approximation schemes for solving the perturbed FitzHugh-Nagumo neuron model. Computers & Mathematics with Applications 143, pages 1-9.
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Manh Tuan Hoang, Thi Kim Quy Ngo & Ha Hai Truong. (2023) A simple method for studying asymptotic stability of discrete dynamical systems and its applications. An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 13:1, pages 10-25.
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Berat KARAAGAC. (2022) A Trigonometric Approach to Time Fractional FitzHugh-Nagumo Model on Nerve Pulse Propagation. Mathematical Sciences and Applications E-Notes 10:3, pages 135-145.
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Pinxia Wu, Kejia Pan, Weiwei Ling & Qihong Wu. (2022) A linearly implicit scheme and fast multigrid solver for 3D Fitzhugh-Nagumo equation. Computers & Mathematics with Applications 117, pages 257-270.
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Huifang Zhou, Zhiqiang Sheng & Guangwei Yuan. (2022) A finite volume scheme preserving the invariant region property for the coupled system of FitzHugh-Nagumo equations on distorted meshes. Computers & Mathematics with Applications 117, pages 39-52.
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Heather Banda, Michael Chapwanya & Phindile Dumani. (2022) Pattern formation in the Holling–Tanner predator–prey model with predator-taxis. A nonstandard finite difference approach. Mathematics and Computers in Simulation 196, pages 336-353.
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C. Koroglu. (2020) Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation. Advances in Difference Equations 2020:1.
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Rui-Xia Li & Guo-Feng Zhang. (2020) Preconditioned iterative methods for the convective FitzHugh–Nagumo equations. Computers & Mathematics with Applications 80:12, pages 2915-2924.
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Manh Tuan Hoang & Oluwaseun Francis Egbelowo. (2020) Numerical dynamics of nonstandard finite difference schemes for a Logistics model with feedback control. ANNALI DELL'UNIVERSITA' DI FERRARA 66:1, pages 51-65.
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Appanah Appadu, Bilge İnan & Yusuf Tijani. (2019) Comparative Study of Some Numerical Methods for the Burgers–Huxley Equation. Symmetry 11:11, pages 1333.
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