Title: Modelling and simulation of transmission lines in a biological neuron

Authors: Charaf Eddine Bailoul; Nour Eddine Alaa

Addresses: Laboratory of Applied Mathematics and Informatics, Faculty of Sciences and Technologies, Cadi Ayyad University, B.P 549 Av.Abdelkarim Elkhattabi, Marrakesh, Morocco ' Laboratory of Applied Mathematics and Informatics, Faculty of Sciences and Technologies, Cadi Ayyad University, B.P 549 Av.Abdelkarim Elkhattabi, Marrakesh, Morocco

Abstract: In this paper, we present a new mathematical model that explains the transmission along a biological neuron. We also present a numerical scheme based on the four order β-method to simulate numerically the transmission. The idea is to couple the β-method of high order with Runge Kutta method in order to get high order schemes without oscillations. Furthermore, various numerical experiments are presented to show the power and efficiency of our proposed model.

Keywords: FDTD; finite difference time domain; beta method; transmission lines; fourth order; mathematical model; biological neuron; electromagnetic propagation; Runge Kutta; discretisation; method of moments; FEM; finite element method.

DOI: 10.1504/IJCBDD.2020.107320

International Journal of Computational Biology and Drug Design, 2020 Vol.13 No.2, pp.224 - 234

Received: 27 Mar 2019
Accepted: 19 Sep 2019
Published online: 13 May 2020 *

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