@Article{JCM-42-1,
author = {Zhang, Gengen and Su, Chunmei},
title = {Uniform Error Bounds of a Conservative Compact Finite Difference Method for the Quantum Zakharov System in the Subsonic Limit Regime},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {1},
pages = {289--312},
abstract = {<p style="text-align: justify;">In this paper, we consider a uniformly accurate compact finite difference method to
solve the quantum Zakharov system (QZS) with a dimensionless parameter $0 &lt; ε ≤ 1,$ which is inversely proportional to the acoustic speed. In the subsonic limit regime, i.e.,
when $0 &lt; ε ≪ 1,$ the solution of QZS propagates rapidly oscillatory initial layers in time,
and this brings significant difficulties in devising numerical algorithm and establishing
their error estimates, especially as $0 &lt; ε ≪ 1.$ The solvability, the mass and energy
conservation laws of the scheme are also discussed. Based on the cut-off technique and
energy method, we rigorously analyze two independent error estimates for the well-prepared
and ill-prepared initial data, respectively, which are uniform in both time and space for $ε ∈ (0, 1]$ and optimal at the fourth order in space. Numerical results are reported to verify
the error behavior.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2204-m2022-0001},
url = {https://global-sci.com/article/84088/uniform-error-bounds-of-a-conservative-compact-finite-difference-method-for-the-quantum-zakharov-system-in-the-subsonic-limit-regime}
}