A HYBRID EXPLICIT-IMPLICIT SCHEME FOR THE TIME-DEPENDENT WIGNER EQUATION  

作　　者：Haiyan Jiang Tiao Lu Xu Yin 

机构地区：[1]Department of Mathematics and Statistics,Beijing Institute of Technology,Beiing 100081,China [2]CAPT,HEDPS,LMAM,IFSA Collaborative Innovation Center of MoE,School of Mathematical Sciences,Peking University,Beijing 100871,China [3]Department of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China

出　　处：《Journal of Computational Mathematics》2021年第1期22-42,共21页计算数学（英文）

基　　金：This research was supported in part by the NSFC(91434201,91630130,11671038,11421101).

摘　　要：This paper designs a hybrid scheme based on finite difference methods and a spectral method for the time-dependent Wigner equation,and gives the error analysis for the full discret ization of its initial value problem.An explicit-implicit time-splitting scheme is used for time integration and the second-order upwind finite difference scheme is used to dis-cretize the advection term.The consistence error and the stability of the full discretization are analyzed.A Fourier spectral method is used to approximate the pseudo-differential operator term and the corresponding error is studied in detail.The final convergence result shows clearly how the regularity of the solution affects the convergence order of the pro-posed scheme.N umerical results are presented for confirming the sharpness of the analysis.The scattering effects of a Gaussian wave packet tunneling through a Gaussian potential barrier are investigated.The evolution of the density function shows that a larger portion of the wave is reflected when the height and the width of the barrier increase.Mathematics subject classification:65M06,65M70.

关 键 词：Finite diference method Spectral method Hybrid scheme Error analysis Wigner equation. 

分 类 号：O17[理学—数学]