Title: A numerical method for a singular perturbation problem arising in the modelling of plasma sheaths

Authors: R.K. Dunne, E. O'Riordan, M.M. Turner

Addresses: School of Mathematical Sciences, Dublin City University, Dublin, Ireland. ' School of Mathematical Sciences, National Center for Plasma Science and Technology, Dublin City University, Dublin, Ireland. ' School of Physical Sciences, National Center for Plasma Science and Technology, Dublin City University, Dublin, Ireland

Abstract: A system of three coupled, non-linear, singularly perturbed differential equations, which arise in the modelling of plasma sheaths, is studied. For one of the component equations theoretical results are given, which show that a numerical method based on a simple linearisation technique, a piecewise-uniform mesh of Shishkin type and a standard upwind finite difference operator generate parameter-uniform numerical approximations. Motivated by this, a numerical method for generating approximations to the solution of the full system of equations is constructed. Numerical results are presented, which indicate that this method is parameter uniform.

Keywords: plasma sheaths; singular perturbation; Shishkin mesh; finite difference method; modelling; differential equations.

DOI: 10.1504/IJCSM.2007.016539

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.2/3/4, pp.322 - 342

Available online: 07 Jan 2008 *

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