ON THE STABILITY OF TIME DISCRETISATIONS FOR THE SEMICONDUCTOR EQUATIONS
- 1 January 1991
- journal article
- Published by Emerald Publishing in COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
- Vol. 10 (1) , 11-25
- https://doi.org/10.1108/eb010327
Abstract
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.Keywords
This publication has 10 references indexed in Scilit:
- Semiconductor device modelling from the numerical point of viewInternational Journal for Numerical Methods in Engineering, 1987
- The Stationary Semiconductor Device EquationsPublished by Springer Nature ,1986
- Transient simulation of silicon devices and circuitsIEEE Transactions on Electron Devices, 1985
- Analysis and Simulation of Semiconductor DevicesPublished by Springer Nature ,1984
- Stability of finite difference approximations to a diffusion–convection equationInternational Journal for Numerical Methods in Engineering, 1980
- Analysis of explicit difference methods for a diffusion‐convection equationInternational Journal for Numerical Methods in Engineering, 1978
- Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’sSIAM Journal on Numerical Analysis, 1977
- Large-signal analysis of a silicon Read diode oscillatorIEEE Transactions on Electron Devices, 1969
- Application of Oscillation Matrices to Diffusion‐Convection EquationsJournal of Mathematics and Physics, 1966
- RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDERThe Quarterly Journal of Mechanics and Applied Mathematics, 1955