A numerical method for a singular perturbation problem arising in the modelling of plasma sheaths Online publication date: Mon, 07-Jan-2008
by R.K. Dunne, E. O'Riordan, M.M. Turner
International Journal of Computing Science and Mathematics (IJCSM), Vol. 1, No. 2/3/4, 2007
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.
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