Time Discretization of a Nonlinear Initial Value Problem
Abstract
Timedependent models of semiconductor devices are readily formulated as a system of three partialdifferential equations in three variables. Each of the equations is linear and well posed for one of the variables; however, if the equations are solved sequentially at each step, a nonlinear instability arises from the coupling terms, unless prohibitively small time steps are used. Three methods are proposed for avoiding such an instability. Convergence and stability results are obtained for each method, and the relative merits of each method are discussed from a practical viewpoint. An example of a computation using one of these methods is included.
 Publication:

Journal of Computational Physics
 Pub Date:
 May 1976
 DOI:
 10.1016/00219991(76)900188
 Bibcode:
 1976JCoPh..21...20M