An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation
Year: 2026
Type: article
Abstract: In the 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.
Author: Ömer Oruç
Institution: Dicle University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7170931897