UNIFORM ERROR BOUNDS OF A CONSERVATIVE COMPACT FINITE DIFFERENCE METHOD FOR THE QUANTUM ZAKHAROV SYSTEM IN THE SUBSONIC LIMIT REGIME  

作　　者：Gengen Zhang Chunmei Su 

机构地区：[1]School of Mathematics and Statistics,Yunnan University,Kunming 650504,China [2]Yau Mathematical Sciences Center,Tsinghua University,Beijing 100084,China

出　　处：《Journal of Computational Mathematics》2024年第1期289-312,共24页计算数学（英文）

基　　金：supported by the Project for the National Natural Science Foundation of China(No.12261103).

摘　　要：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 forε∈(0,1]and optimal at the fourth order in space.Numerical results are reported to verify the error behavior.

关 键 词：Quantum Zakharov system Subsonic limit Compact finite difference method Uniformly accurate Error estimate 

分 类 号：O24[理学—计算数学]