A nonstandard finite difference scheme for the drift-diffusion system

Pages: 558 - 563, Issue Special, September 2009

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Ronald E. Mickens - Department of Physics, Clark Atlanta University, Atlanta, GA 30314, United States (email)

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.

Keywords:  Drift-diffusion systems, nonlinear PDE's, reaction-diffusion equations, laser physics
Mathematics Subject Classification:  Primary: 65M06; Secondary: 78A60, 80-08

Received: June 2008;      Revised: May 2009;      Published: September 2009.