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 by Xin and Xu (2000).

翻译：本文研究了半直线上线性阻尼波动方程的半离散格式及隐式中点格式的稳定性问题，其中空间边界对极限方程具有特征性。所提出的格式采用了一种离散边界条件，该条件旨在保证初边值问题的一致稳定性，且与源项的刚性程度或空间步长无关。基于Xin与Xu（2000）所分析的连续框架，本文利用求和-分部（SBP）技术与同步逼近项（SAT）罚函数技术，建立了半离散格式的稳定性估计。