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Error Analysis of BDF2 Scheme for the Boussinesq System Based on Exponential Scalar Auxiliary Variable

  • Huanhuan Li , Meng Li and Xianbing Luo ORCID logo EMAIL logo
Published/Copyright: October 11, 2025

Abstract

A linear BDF2 numerical scheme is proposed to solve the Boussinesq system. By using the exponential scalar auxiliary variable (E-SAV) approach, we explicitly deal with the nonlinear terms of the Boussinesq system, and decouple the velocity and temperature in the numerical simulation. These numerical scheme is unconditionally stable. We give rigorous error analysis for the velocity and temperature. Numerical experiment is performed to verify the proposed numerical scheme.

MSC 2020: 65M12; 65M15; 65M60

Award Identifier / Grant number: 12461076

Funding statement: The authors would like to thank National Natural Science Foundation of China (No. 12461076) and Guizhou University Doctoral Fund ([2022] No. 15).

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Received: 2024-02-21
Revised: 2025-06-29
Accepted: 2025-09-13
Published Online: 2025-10-11

© 2025 Institute of Mathematics of the National Academy of Science of Belarus, published by De Gruyter, Berlin/Boston

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