A Trigonometric Approach to Time Fractional FitzHugh-Nagumo Model on Nerve Pulse Propagation

Year 2022, Volume: 10 Issue: 3, 135 - 145, 09.09.2022

Berat Karaagac

https://doi.org/10.36753/mathenot.1025072

Cited By: 1

Abstract

The aim of this paper is to put on display the numerical solutions and dynamics
of time fractional Fitzhugh-Nagumo model, which is an important nonlinear
reaction-diffusion equation. For this purpose, finite element method based
on trigonometric cubic B-splines are used to obtain numerical solutions of the model.
In this model, the derivative which is fractional order is taken in terms of Caputo.
Thus, time dicretization is made using $L1$ algorithm for Caputo
derivative and space discretization is made using trigonometric cubic B-
spline basis. Also, the non-linear term in the model is linearized by the
Rubin Graves type linearization. The error norms are calculated for measuring the
accuracy of the finite element method. The comparison of numerical and
exact solutions are exhibited via tables and graphics.

Keywords

Time fractional Fitzhugh-Nagumo model, finite element method, collocation

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