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