Stability and accuracy of a pseudospectral scheme for the Wigner function equation

Andrea Thomann (1) , Alfio Borzì (1)

1 JMU - Julius-Maximilians-Universität Würzburg

A pseudospectral scheme with centred time-differencing for solving the Wigner function equation is investigated. Stability, second-order accuracy in time, and spectral accuracy in space are proved for the Wigner function 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.

Domaines: Mathématiques [math]

Andrea Thomann, Alfio Borzì. Stability and accuracy of a pseudospectral scheme for the Wigner function equation. Numerical Methods for Partial Differential Equations, 2017, 33 (1), pp.62-87. ⟨10.1002/num.22072⟩. ⟨hal-03587242⟩