ON THE STABILITY OF TIME DISCRETISATIONS FOR THE SEMICONDUCTOR EQUATIONS
Paul WILD · COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering · 1991
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.