Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs
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- by Dongfang Li, Xiaoxi Li and Zhimin Zhang;
- Math. Comp. 92 (2023), 117-146
- DOI: https://doi.org/10.1090/mcom/3766
- Published electronically: August 19, 2022
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Abstract:
Spatial discretizations of time-dependent partial differential equations usually result in a large system of semi-linear and stiff ordinary differential equations. Taking the structures into account, we develop a family of linearly implicit and high order accurate schemes for the time discretization, using the idea of implicit-explicit Runge-Kutta methods and the relaxation techniques. The proposed schemes are monotonicity-preserving/conservative for the original problems, while the previous linearized methods are usually not. We also discuss the linear stability and strong stability preserving (SSP) property of the new relaxation methods. Numerical experiments on several typical models are presented to confirm the effectiveness of the proposed methods.References
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Bibliographic Information
- Dongfang Li
- Affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China; and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
- Email: dfli@mail.hust.edu.cn
- Xiaoxi Li
- Affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
- Email: xiaoxili@hust.edu.cn
- Zhimin Zhang
- Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
- Email: ag7761@wayne.edu
- Received by editor(s): September 2, 2021
- Received by editor(s) in revised form: March 13, 2022, and May 22, 2022
- Published electronically: August 19, 2022
- Additional Notes: The research was partially supported by NSFC (grants nos. 11771162, 11971010, 11871092).
- © Copyright 2022 American Mathematical Society
- Journal: Math. Comp. 92 (2023), 117-146
- MSC (2020): Primary 65L06, 65L20, 65M12
- DOI: https://doi.org/10.1090/mcom/3766
- MathSciNet review: 4496961