Browsing by Author "Ali, Ihteram"

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    Radial Basis Functions Approximation Method for Time-Fractional FitzHugh-Nagumo Equation
    (Mdpi, 2023) Alam, Mehboob; Salahshour, Soheıl; Ali, Ihteram; Ebadi, M. J.; Salahshour, Soheil
    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 infinity, and Lrms.