Analysis of a fast element-free Galerkin method for the multi-term time-fractional diffusion equation

Zesen Hu and Xiaolin Li

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 223, issue C, 677-692

Abstract: In this paper, a fast element-free Galerkin (EFG) method is proposed for solving the multi-term time-fractional diffusion equation (TFDE). Through the use of the multi-term L2−1σ formula to discrete the multi-term Caputo time-fractional derivative, a fast second-order scheme is presented for the temporal discretization, and then the EFG method is used to perform the spatial discretization. The stability of the temporal discretization scheme is discussed. By verifying the fractional Grönwall inequality, the global error of the proposed EFG method for the multi-term TFDE is analyzed in theory. Numerical results validate the theoretical results and the effectiveness of the method.

Keywords: Meshless methods; Element-free Galerkin method; Fractional diffusion equation; Multi-term fractional derivatives; Error analysis; Fast algorithm (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:223:y:2024:i:c:p:677-692

DOI: 10.1016/j.matcom.2024.05.008

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