TY - JOUR
T1 - A Hybrid Explicit-Implicit Scheme for the Time-Dependent Wigner Equation
AU - Jiang , Haiyan
AU - Lu , Tiao
AU - Yin , Xu
JO - Journal of Computational Mathematics
VL - 1
SP - 22
EP - 42
PY - 2020
DA - 2020/09
SN - 39
DO - http://doi.org/10.4208/jcm.1906-m2018-0081
UR - https://global-sci.org/intro/article_detail/jcm/18276.html
KW - Finite difference method, Spectral method, Hybrid scheme, Error analysis, Wigner equation.
AB - <p style="text-align: justify;">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 discretize 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 proposed 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.</p>