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

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Date

2023

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Mdpi

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Abstract

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.

Description

Ebadi, Mohammad Javad/0000-0002-1324-6953; Alam, Mehboob/0000-0001-7721-7767

Keywords

fractional differential equation, meshless method, radial basis functions, FitzHugh-Nagumo equation, stability

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1

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Q1

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Volume

7

Issue

12

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