A numerical method for a singular perturbation problem arising in the modelling of plasma sheaths
type: Item
instance of: scholarly article
title: A numerical method for a singular perturbation problem arising in the modelling of plasma sheaths
zbMATH Open document ID: 1185.65206
DOI: 10.1504/IJCSM.2007.016539
author: R. K. Dunne
author: Eugene O'Riordan
author: M. M. Turner
published in: International Journal of Computing Science and Mathematics
publication date: 2010-05-05T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 5703884
zbMATH Keywords: plasma sheaths
zbMATH Keywords: singular perturbation
zbMATH Keywords: Shishkin mesh
zbMATH Keywords: finite difference method
zbMATH Keywords: modelling
zbMATH Keywords: differential equations
MaRDI profile type: Publication
full work available at URL: ijcsm.2007.016539
OpenAlex ID: W1989653482
description: scientific article; zbMATH DE number 5703884