A nonstandard finite difference scheme for the drift-diffusion system

Ronald E. Mickens

doi:10.3934/proc.2009.2009.558

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2009, Volume 2009: 558-563. Doi: 10.3934/proc.2009.2009.558 open access

This issue Previous Article Stochastic inclusions with non-continuous set-valued operators Next Article On the solvability of some fourth-order equations with functional boundary conditions

A nonstandard finite difference scheme for the drift-diffusion system

Ronald E. Mickens^1,

1.
Department of Physics, Clark Atlanta University, Atlanta, GA 30314

Received: May 31, 2008

Revised: April 30, 2009

Published: August 2009

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Abstract

We derive a nonstandard finite difference scheme for the coupled, nonlinear PDE's modeling laser generated electrons and holes in a semiconductor. Our scheme has the essential feature of giving numerical solutions for which the charge densities are non-negative. Many of the standard schemes do not have this physically required property.

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Mathematics Subject Classification: Primary: 65M06; Secondary: 78A60, 80-08.

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