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Research Article | Open Access

Mixed finite element method for a time-fractional generalized Rosenau-RLW-Burgers equation

Ning Yang, Yang Liu( )
School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China
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Abstract

In this article, the time-fractional generalized Rosenau-RLW-Burgers equation is numerically solved, where the generalized BDF2- θ is used to discretize the temporal direction, and the mixed finite element method is applied to the spatial direction. The stability of the fully discrete scheme is proven. Finally, the effectiveness of the numerical scheme is verified through some numerical examples, and the singularity of nonsmooth solutions in the initial time layer is effectively resolved by adding the correction term.

Keywords

time-fractional generalized Rosenau-RLW-Burgers equationmixed finite element methodgeneralized BDF2-θstabilitycorrection termweak singularity
CLC number: 24A33, 65M60, 65N30

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AIMS Mathematics
Volume 10 Issue 1,
January 2025
Pages 1757-1778
DOI: 10.3934/math.2025080

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Cite this article:
Yang N, Liu Y. Mixed finite element method for a time-fractional generalized Rosenau-RLW-Burgers equation. AIMS Mathematics, 2025, 10(1): 1757-1778. https://doi.org/10.3934/math.2025080

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Received: 28 October 2024
Revised: 05 January 2025
Accepted: 14 January 2025
Published: 15 January 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)