Tension spline method for solution of Fitzhugh-Nagumo equation

被引：6

作者：

Shekarabi, H. S. ^{[1
]}

Aqamohamadi, M. ^{[2
]}

Rashidinia, J. ^{[3
]}

机构：

[1] Islamic Azad Univ, East Tehran Branch, Young Researchers & Elite Club, Tehran, Iran

[2] Islamic Azad Univ, Dept Math, Karaj, Iran

[3] Iran Univ Sci & Technol, Sch Math, Tehran, Iran

来源：

TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE | 2018年 / 172卷 / 03期

关键词：

Nonlinear spline; Finite difference; Fitzhugh-Nagumo equation; Energy method;

D O I：

10.1016/j.trmi.2018.02.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2018 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V.

引用

页码：571 / 581

页数：11

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