Implicit one‐step methods for the system of differential equations arising from a space discretisation of the semiconductor equations are considered. It is shown that mere spectral conditions like A‐stability or L‐stability do not give a reliable answer to the behaviour of the numerical solution. Rather, positivity arguments for the corresponding rational matrix functions play an important role.
WILD, P. (1991), "ON THE STABILITY OF TIME DISCRETISATIONS FOR THE SEMICONDUCTOR EQUATIONS", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 10 No. 1, pp. 11-25. https://doi.org/10.1108/eb010327
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