Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation with Collocation Method

Year 2025, Volume: 8 Issue: 3, 180 - 186, 30.09.2025

Derya Yıldırım Sucu , Seydi Battal Gazi Karakoç , Müjdet Güngör

https://doi.org/10.33401/fujma.1617563

Abstract

In the present paper, an accurate and reliable numerical scheme has been created for solving FitzHugh-Nagumo (F-N) equation which is a mathematical model that describes the spiking behaviorof neurons. For this, the scheme is constructed on the collocation finite element method using the septic B-spline technique. $L_{2}$ and $L_{\infty }$ error norms are computed to check the validity and reliability of the current method. Tables and graphs are used to demonstrate the effectiveness of the solutions produced. The obtained numerical results are compared with other existing numerical methods to validate the accuracy and efficiency of the proposed scheme. Numerical experiments demonstrate that our scheme provides highly accurate solutions for the F-N equation and shows highly compatible with other numerical techniques in terms of accuracy and efficiency.

Keywords

Fitzhugh-Nagumo equation , Finite element method , Collocation , Septic B-spline

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