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

Published Online:pp 322-342https://doi.org/10.1504/IJCSM.2007.016539

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