TY - JOUR
T1 - Uniform Error Bounds of a Conservative Compact Finite Difference Method for the Quantum Zakharov System in the Subsonic Limit Regime
AU - Zhang , Gengen
AU - Su , Chunmei
JO - Journal of Computational Mathematics
VL - 1
SP - 289
EP - 312
PY - 2023
DA - 2023/12
SN - 42
DO - http://doi.org/10.4208/jcm.2204-m2022-0001
UR - https://global-sci.org/intro/article_detail/jcm/22161.html
KW - Quantum Zakharov system, Subsonic limit, Compact finite difference method,
Uniformly accurate, Error estimate.
AB - <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>