TY - JOUR T1 - Interior Layers in a Reaction-Diffusion Equation with a Discontinuous Diffusion Coefficient JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 444 EP - 461 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/730.html KW - Diffusion Reaction Equations, Singularly Perturbed Differential Equations, Finite Difference Methods on Fitted Meshes. AB -

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.