Tension spline method for solution of Fitzhugh–Nagumo equation
One of the most widely studied biological systems with excitable behavior is neural communication by nerve cells via electrical signaling. The Fitzhugh–Nagumo equation is a simplification of the Hodgin–Huxley model (Hodgin and Huxley, 1952) [24] for the membrane potential of a nerve axon. In this pa...
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doaj-af3958fe4dce443fa80ab8032f6208d52020-11-24T21:49:14ZengElsevierTransactions of A. Razmadze Mathematical Institute2346-80922018-12-011723571581Tension spline method for solution of Fitzhugh–Nagumo equationH.S. Shekarabi0M. Aqamohamadi1J. Rashidinia2Young Researchers and Elite Club, East Tehran Branch, Islamic Azad University, Tehran, Iran; Corresponding author.Department of Mathematics, Islamic Azad University, Karaj, IranSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran, IranOne of the most widely studied biological systems with excitable behavior is neural communication by nerve cells via electrical signaling. The Fitzhugh–Nagumo equation is a simplification of the Hodgin–Huxley model (Hodgin and Huxley, 1952) [24] for the membrane potential of a nerve axon. In this paper we developed a three time-level implicit method by using tension spline function. The resulting equations are solved by a tri-diagonal solver. We described the mathematical formulation procedure in detail. The stability of the presented method is investigated. Results of numerical experiments verify the theoretical behavior of the orders of convergence. MSC: 65M06, 1299, Keywords: Nonlinear spline, Finite difference, Fitzhugh–Nagumo equation, Energy methodhttp://www.sciencedirect.com/science/article/pii/S2346809217300971 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
H.S. Shekarabi M. Aqamohamadi J. Rashidinia |
spellingShingle |
H.S. Shekarabi M. Aqamohamadi J. Rashidinia Tension spline method for solution of Fitzhugh–Nagumo equation Transactions of A. Razmadze Mathematical Institute |
author_facet |
H.S. Shekarabi M. Aqamohamadi J. Rashidinia |
author_sort |
H.S. Shekarabi |
title |
Tension spline method for solution of Fitzhugh–Nagumo equation |
title_short |
Tension spline method for solution of Fitzhugh–Nagumo equation |
title_full |
Tension spline method for solution of Fitzhugh–Nagumo equation |
title_fullStr |
Tension spline method for solution of Fitzhugh–Nagumo equation |
title_full_unstemmed |
Tension spline method for solution of Fitzhugh–Nagumo equation |
title_sort |
tension spline method for solution of fitzhugh–nagumo equation |
publisher |
Elsevier |
series |
Transactions of A. Razmadze Mathematical Institute |
issn |
2346-8092 |
publishDate |
2018-12-01 |
description |
One of the most widely studied biological systems with excitable behavior is neural communication by nerve cells via electrical signaling. The Fitzhugh–Nagumo equation is a simplification of the Hodgin–Huxley model (Hodgin and Huxley, 1952) [24] for the membrane potential of a nerve axon. In this paper we developed a three time-level implicit method by using tension spline function. The resulting equations are solved by a tri-diagonal solver. We described the mathematical formulation procedure in detail. The stability of the presented method is investigated. Results of numerical experiments verify the theoretical behavior of the orders of convergence. MSC: 65M06, 1299, Keywords: Nonlinear spline, Finite difference, Fitzhugh–Nagumo equation, Energy method |
url |
http://www.sciencedirect.com/science/article/pii/S2346809217300971 |
work_keys_str_mv |
AT hsshekarabi tensionsplinemethodforsolutionoffitzhughnagumoequation AT maqamohamadi tensionsplinemethodforsolutionoffitzhughnagumoequation AT jrashidinia tensionsplinemethodforsolutionoffitzhughnagumoequation |
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1725888592521199616 |