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

• 来源期刊: 计算数学（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 22-42
• 页数: 21页
• 语种: 英文
• DOI: 10.4208/jcm.1906-m2018-0081

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 discretization 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.Numerical 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.