Engineering Simulation: An International Journal of Electrical, Electronic and other Physical Systems, 12, 856--865, 1995
The paper considers the application of semi-implicit finite-difference schemes and the flow correction method to mathematical modelling of semiconductor devices based on nonlocal models of the quasi-hydrodynamic type in the nonstationary case. It is proved that the maximum principle holds for the earlier constructed semi-implicit schemes. It is suggested to use the flow correction techniques to attain a compromise between the positiveness of the solution and the monotonicity of the numerical method. Numerical calculation results are presented to confirm the theoretical conclusions.
