A stiffly stable semi-discrete scheme for the damped wave equation on the half-line using SBP and SAT techniques

2024/11/25 by Thi Hoai Thuong Nguyen, Nguyen, Thi Hoai Thuong, Benjamin Boutin +1
Engineering · #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Vibration and Dynamic Analysis

paper · pdf · doi:10.48550/arxiv.2411.16388

openalex publication_date 2024/11/25 · openalex created_date 2025/08/06 · openalex updated_date 2026/08/01

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 by Xin and Xu (2000).

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