A numerical method for a singular perturbation problem arising in the modelling of plasma sheaths. (8th January 2008)

• Record Type: Journal Article
• Authors: Dunne, R.K.; O'Riordan, E.; Turner, M.M.
• Is Part Of: International journal of computing science and mathematics. Volume 1:Number 2/3/4(2007)
• Page Start: 322
• Page End: 342
• Publication Date: 2008-01-08
• Subjects: plasma sheaths -- singular perturbation -- Shishkin mesh -- finite difference method -- modelling -- differential equations; Mathematics -- Periodicals; Computer science -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.285
• Languages: English
• ISSNs: 1752-5055

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.