An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation

Ömer Oruç

doi:10.33187/jmsm.1931851

An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation

Abstract

In present study, we proposed an efficient numerical approach for Fitzhugh-Nagumo equation which is a nonlinear partial differential equation and has many applications in various branches of science. The suggested numerical method uses a meshless method called as enriched radial point interpolation method for discretization of space variables which forms a large system of ordinary differential equations (ODEs). In general, the acquired ODEs system is stiff therefore to obtain good results a small time step size should be used for time integration. In order to put relaxation on the time step size a splitting approach is utilized which divide the equation into non-stiff and stiff terms. Then a Rosenbrock method is devised to solve stiff term and a strong stability preserving Runge Kutta method is proposed to solve non-stiff term. To show efficiency of the suggested method some numerical tests are fulfilled and acquired results are compared with available numerical techniques in literature such as collocation, meshless and finite difference methods, and with exact solution. The comparisons reveal accuracy of the suggested method.

Keywords

Enriched radial point interpolation method, Meshless method, Rosenbrock method, Fitzhugh-Nagumo equation, Time splitting

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Details

Primary Language

English

Subjects

Partial Differential Equations, Applied Mathematics (Other)

Journal Section

Research Article

Authors

Ömer Oruç ^*
0000-0002-6655-3543
Türkiye

Early Pub Date

July 24, 2026

Publication Date

-

Submission Date

April 16, 2026

Acceptance Date

July 20, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.33187/jmsm.1931851

IZ

https://izlik.org/JA59TY24RJ

APA

Oruç, Ö. (2026). An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation. Journal of Mathematical Sciences and Modelling, Advanced Online Publication, 152-161. https://doi.org/10.33187/jmsm.1931851

AMA

1.Oruç Ö. An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation. Journal of Mathematical Sciences and Modelling. 2026;(Advanced Online Publication):152-161. doi:10.33187/jmsm.1931851

Chicago

Oruç, Ömer. 2026. “An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation”. Journal of Mathematical Sciences and Modelling, no. Advanced Online Publication: 152-61. https://doi.org/10.33187/jmsm.1931851.

EndNote

Oruç Ö (July 1, 2026) An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation. Journal of Mathematical Sciences and Modelling Advanced Online Publication 152–161.

IEEE

[1]Ö. Oruç, “An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation”, Journal of Mathematical Sciences and Modelling, no. Advanced Online Publication, pp. 152–161, July 2026, doi: 10.33187/jmsm.1931851.

ISNAD

Oruç, Ömer. “An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation”. Journal of Mathematical Sciences and Modelling. Advanced Online Publication (July 1, 2026): 152-161. https://doi.org/10.33187/jmsm.1931851.

JAMA

1.Oruç Ö. An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation. Journal of Mathematical Sciences and Modelling. 2026;:152–161.

MLA

Oruç, Ömer. “An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation”. Journal of Mathematical Sciences and Modelling, no. Advanced Online Publication, July 2026, pp. 152-61, doi:10.33187/jmsm.1931851.

Vancouver

1.Ömer Oruç. An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation. Journal of Mathematical Sciences and Modelling. 2026 Jul. 1;(Advanced Online Publication):152-61. doi:10.33187/jmsm.1931851