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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Main Authors: H.S. Shekarabi, M. Aqamohamadi, J. Rashidinia
Format: Article
Language:English
Published: Elsevier 2018-12-01
Series:Transactions of A. Razmadze Mathematical Institute
Online Access:http://www.sciencedirect.com/science/article/pii/S2346809217300971
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spelling 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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