Year: 2010
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 444–461
Abstract
In this paper a problem arising in the modelling of semiconductor devices motivates the study of singularly perturbed differential equations of reaction-diffusion type with discontinuous data. The solutions of such problems typically contain interior layers where the gradient of the solution changes rapidly. Parameter-uniform methods based on piecewise-uniform Shishkin meshes are constructed and analysed for such problems. Numerical results are presented to support the theoretical results and to illustrate the benefits of using a piecewise-uniform Shishkin mesh over the use of uniform meshes in the simulation of a simple semiconductor device.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-730
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 444–461
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Diffusion Reaction Equations Singularly Perturbed Differential Equations Finite Difference Methods on Fitted Meshes.