@Article{IJNAM-7-507,
author = {T. Linss and N. Madden},
title = {Analysis of an Alternating Direction Method Applied to Singularly Perturbed Reaction-Diffusion Problems},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2010},
volume = {7},
number = {3},
pages = {507--519},
abstract = {<p style="text-align: justify;">We present an analysis of an Alternating Direction Implicit (ADI)
scheme for a linear, singularly perturbed reaction-diffusion equation. By providing an expression for the error that separates the temporal and spatial components, we can use existing results for steady-state problems to give a succinct analysis for the time-dependent problem, and that generalizes for various
layer-adapted meshes. We report the results of numerical experiments that
support the theoretical findings. In addition, we provide a numerical comparison between the ADI and Euler techniques, as well details of the computational
advantage gained by parallelizing the algorithm.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/734.html}
}