Radial Basis Functions Approximation Method for Time-Fractional FitzHugh–Nagumo Equation

In this paper, a numerical approach employing radial basis functions has been applied to solve time-fractional FitzHugh–Nagumo equation. Spatial approximation is achieved by combining radial basis functions with the collocation method, while temporal discretization is accomplished using a finite dif...

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Bibliographic Details
Published in:Fractal and fractional 2023-12, Vol.7 (12), p.882
Main Authors: Alam, Mehboob, Haq, Sirajul, Ali, Ihteram, Ebadi, M. J., Salahshour, Soheil
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Collocation methods
Eigenvalues
Exact solutions
Finite difference method
Finite element method
Finite volume method
FitzHugh–Nagumo equation
fractional differential equation
Investigations
Laplace transforms
Mesh generation
meshless method
Numerical analysis
Radial basis function
radial basis functions
stability
Stability analysis
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Summary:In this paper, a numerical approach employing radial basis functions has been applied to solve time-fractional FitzHugh–Nagumo equation. Spatial approximation is achieved by combining radial basis functions with the collocation method, while temporal discretization is accomplished using a finite difference scheme. To evaluate the effectiveness of this method, we first conduct an eigenvalue stability analysis and then validate the results with numerical examples, varying the shape parameter c of the radial basis functions. Notably, this method offers the advantage of being mesh-free, which reduces computational overhead and eliminates the need for complex mesh generation processes. To assess the method’s performance, we subject it to examples. The simulated results demonstrate a high level of agreement with exact solutions and previous research. The accuracy and efficiency of this method are evaluated using discrete error norms, including L2, L∞, and Lrms.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7120882