Abstract
A pseudospectral scheme with centered time‐differencing for solving the Wigner function (WF) equation is investigated. Stability, second‐order accuracy in time, and spectral accuracy in space are proved for the WF equation with a potential in a periodic setting. In addition, normalization and energy conservation properties, and Ehrenfest's theorem are discussed. Numerical experiments are presented to validate the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 62–87, 2017
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