Most simulators use a Newton-like method for solving the semiconductor device equations. The linearized system obtained by this method is then solved either directly or iteratively. However, it is also possible to use an explicit method instead of the implicit Newton method. This method was first introduced by Kurata and Nakamura (see ibid., vol. 11, no. 8, p. 1013-22, 1992) for the semiconductor equations. The authors revise and improve this explicit method and show the properties and limitations of the algorithm. The main limitation of the method is the long computation time needed. However, the method benefits from a very simple algorithm, low memory requirements, and highly parallel properties.>