Radial Basis Function Finite Difference method for solving the generalized time-fractional Burgers equation with three types of boundary conditions

Junping Guan, Kaysar Rahman and Ziyu Guo

Chaos, Solitons & Fractals, 2025, vol. 199, issue P3

Abstract: In this paper, we propose an effective numerical method for solving generalized time-fractional Burgers equation (GTFBE) with Dirichlet, Neumann, and Periodic boundary conditions respectively. The time Caputo fractional derivative is discretized by employing the L2-1σ formula, and the spatial derivative is approximated by the second-order convergence Radial Basis Function Finite Difference (RBF-FD) scheme. The order of convergence of the proposed scheme is O(τ2+h2), where τ and h are the time and spatial step sizes, respectively. The convergence and unconditionable stability of the method are theoretically analyzed. The proposed method is implemented on various examples and numerical results are compared with those of other existing methods in the literature. The results show that our proposed methods are more accurate than the other methods.

Keywords: Time-fractional Burgers equation; L2-1σ formula; Caputo fractional derivative; RBF-FD method (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925007672

DOI: 10.1016/j.chaos.2025.116754

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