Singularly perturbed reactiondiffusion problems with discontinuities in the initial and/or the boundary data
Abstract
Numerical approximations to the solutions of three different problem classes of singularly perturbed parabolic reactiondiffusion problems, each with a discontinuity in the bound\aryinitial data, are generated. For each problem class, an analytical function associated with the discontinuity in the data, is identified. Parameteruniform numerical approximations to the difference between the analytical function and the solution of the singularly perturbed problem are generated using piecewiseuniform Shishkin meshes. Numerical results are given to illustrate all the theoretical error bounds established in the paper.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.04016
 Bibcode:
 2018arXiv181104016G
 Keywords:

 Mathematics  Numerical Analysis;
 65M06;
 65M12;
 65M15
 EPrint:
 8 figures