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

• Published in: Fractal and fractional Vol. 7; no. 12; p. 882
• Main Authors: Alam, Mehboob, Haq, Sirajul, Ali, Ihteram, Ebadi, M. J., Salahshour, Soheil
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.12.2023
• 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
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract7120882

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.