Uniform Error Bounds of a Conservative Compact Finite Difference Method for the Quantum Zakharov System in the Subsonic Limit Regime
Year: 2024
Author: Gengen Zhang, Chunmei Su
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 289–312
Abstract
In this paper, we consider a uniformly accurate compact finite difference method to solve the quantum Zakharov system (QZS) with a dimensionless parameter $0 < ε ≤ 1,$ which is inversely proportional to the acoustic speed. In the subsonic limit regime, i.e., when $0 < ε ≪ 1,$ 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 $0 < ε ≪ 1.$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2204-m2022-0001
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 289–312
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Quantum Zakharov system Subsonic limit Compact finite difference method Uniformly accurate Error estimate.