A numerical method for a singular perturbation problem arising in the modelling of plasma sheaths. (8th January 2008) - Dunne, R.K.; O'Riordan, E.; Turner, M.M.
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.