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

Derya Yıldırım Sucu; Seydi Battal Gazi Karakoç; Müjdet Güngör

doi:10.33401/fujma.1617563

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

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

References

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Details

Primary Language

English

Subjects

Experimental Mathematics , Numerical Analysis , Finite Element Analysis

Journal Section

Research Article

Authors

Derya Yıldırım Sucu
0000-0001-8396-8081
Türkiye

Seydi Battal Gazi Karakoç ^*
0000-0002-2348-4170
Türkiye

Müjdet Güngör
0000-0001-8327-2543
Türkiye

Publication Date

September 30, 2025

Submission Date

January 10, 2025

Acceptance Date

September 29, 2025

Published in Issue

Year 1970 Volume: 8 Number: 3

DOI

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

IZ

https://izlik.org/JA55GX79SS

Cite

RIS / Bibtex

APA

Yıldırım Sucu, D., Karakoç, S. B. G., & Güngör, M. (2025). Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation with Collocation Method. Fundamental Journal of Mathematics and Applications, 8(3), 180-186. https://doi.org/10.33401/fujma.1617563

AMA

1.Yıldırım Sucu D, Karakoç SBG, Güngör M. Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation with Collocation Method. Fundam. J. Math. Appl. 2025;8(3):180-186. doi:10.33401/fujma.1617563

Chicago

Yıldırım Sucu, Derya, Seydi Battal Gazi Karakoç, and Müjdet Güngör. 2025. “Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation With Collocation Method”. Fundamental Journal of Mathematics and Applications 8 (3): 180-86. https://doi.org/10.33401/fujma.1617563.

EndNote

Yıldırım Sucu D, Karakoç SBG, Güngör M (September 1, 2025) Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation with Collocation Method. Fundamental Journal of Mathematics and Applications 8 3 180–186.

IEEE

[1]D. Yıldırım Sucu, S. B. G. Karakoç, and M. Güngör, “Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation with Collocation Method”, Fundam. J. Math. Appl., vol. 8, no. 3, pp. 180–186, Sept. 2025, doi: 10.33401/fujma.1617563.

ISNAD

Yıldırım Sucu, Derya - Karakoç, Seydi Battal Gazi - Güngör, Müjdet. “Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation With Collocation Method”. Fundamental Journal of Mathematics and Applications 8/3 (September 1, 2025): 180-186. https://doi.org/10.33401/fujma.1617563.

JAMA

1.Yıldırım Sucu D, Karakoç SBG, Güngör M. Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation with Collocation Method. Fundam. J. Math. Appl. 2025;8:180–186.

MLA

Yıldırım Sucu, Derya, et al. “Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation With Collocation Method”. Fundamental Journal of Mathematics and Applications, vol. 8, no. 3, Sept. 2025, pp. 180-6, doi:10.33401/fujma.1617563.

Vancouver

1.Derya Yıldırım Sucu, Seydi Battal Gazi Karakoç, Müjdet Güngör. Investigation on the New Numerical Soliton Solutions of FitzHugh-Nagumo Equation with Collocation Method. Fundam. J. Math. Appl. 2025 Sep. 1;8(3):180-6. doi:10.33401/fujma.1617563

Cited By

Computational Study of Singularly Perturbed Neurodynamical Models via Cubic B-Spline

Axioms

https://doi.org/10.3390/axioms15010012