| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2557 - 2581 | |
| DOI | https://doi.org/10.1051/m2an/2025069 | |
| Published online | 17 September 2025 | |
A stiffly stable semi-discrete scheme for the damped wave equation on the half-line using SBP and SAT techniques
1
Department of Analysis, Faculty of Mathematics and Computer Science, University of Science, 227, Nguyen Van Cu, Cho Quan Ward, Ho Chi Minh City 700000, Vietnam
2
Vietnam National University, Ho Chi Minh City, Vietnam
3
Univ Rennes, CNRS, IRMAR – UMR 6625, F-35000 Rennes, France
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
20
November
2024
Accepted:
1
August
2025
Abstract
This paper investigates the stability of both the semi-discrete and the implicit central scheme for the linear damped wave equation on the half-line, where the spatial boundary is characteristic for the limiting equation. The proposed schemes incorporate a discrete boundary condition designed to guarantee the uniform stability of the IBVP, regardless of the stiffness of the source term or the spatial step size. Stability estimates for the semi-discrete scheme are established using the summation-by-parts (SBP) and simultaneous-approximation-term (SAT) penalty techniques, building on the continuous framework analyzed in Xin and Xu [J. Differ. Equ. 167 (2000) 388–437].
Mathematics Subject Classification: 35L50 / 65M06 / 65M12
Key words: Hyperbolic relaxation system / characteristic boundaries / damped wave equation / stiff stability / summation by parts operators / simultaneous approximation term / central schemes / energy estimates
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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