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New additive difference method for solving semiconductor problems

Abstract We propose a new approach to the construction of conservative monotone difference schemes for two-dimensional parabolic second-order equations with divergent form of the terms with first derivatives. These equations appear in a drift diffusion model which is a classical one for describing the semiconductor processes. Using the approach proposed, we obtain a difference scheme for the equations of the drift diffusion model and prove the convergence of this scheme in the grid norm L2 at the rate of Ο(τ + h).