Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation
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- by Jingwei Hu and Ruiwen Shu;
- Math. Comp. 94 (2025), 209-240
- DOI: https://doi.org/10.1090/mcom/3967
- Published electronically: March 28, 2024
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Abstract:
Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a small parameter $\varepsilon$. In this work, we prove rigorously the uniform stability and uniform accuracy of a class of IMEX-RK schemes for a linear hyperbolic system with stiff relaxation. The result we obtain is optimal in the sense that it holds regardless of the value of $\varepsilon$ and the order of accuracy is the same as the design order of the original scheme, i.e., there is no order reduction.References
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Bibliographic Information
- Jingwei Hu
- Affiliation: Department of Applied Mathematics, University of Washington, Seattle, Washington 98195
- MR Author ID: 933436
- ORCID: 0000-0001-6792-6711
- Email: hujw@uw.edu
- Ruiwen Shu
- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 1204137
- Email: ruiwen.shu@uga.edu
- Received by editor(s): June 14, 2023
- Received by editor(s) in revised form: November 17, 2023
- Published electronically: March 28, 2024
- Additional Notes: The work of the first author was partially supported by NSF DMS-2153208, AFOSR FA9550-21-1-0358, and DOE DE-SC0023164. The work of the second author was supported by the Advanced Grant Nonlocal-CPD (Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization) of the European Research Council Executive Agency (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 883363).
- © Copyright 2024 American Mathematical Society
- Journal: Math. Comp. 94 (2025), 209-240
- MSC (2020): Primary 35L03, 65L04, 65L06, 65M12
- DOI: https://doi.org/10.1090/mcom/3967