American Institute of Mathematical Sciences

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2009, 2009(Special): 558-563. doi: 10.3934/proc.2009.2009.558

A nonstandard finite difference scheme for the drift-diffusion system

Ronald E. Mickens 1,

1. 

Department of Physics, Clark Atlanta University, Atlanta, GA 30314, United States

Received  June 2008 Revised  May 2009 Published  September 2009

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.
Keywords: laser physics, reaction-diffusion equations, Drift-diffusion systems, nonlinear PDE's.
Mathematics Subject Classification: Primary: 65M06; Secondary: 78A60, 80-08.
Citation: Ronald E. Mickens. A nonstandard finite difference scheme for the drift-diffusion system. Conference Publications, 2009, 2009 (Special) : 558-563. doi: 10.3934/proc.2009.2009.558
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