TY - JOUR
T1 - Analysis of an Alternating Direction Method Applied to Singularly Perturbed Reaction-Diffusion Problems
AU - T. Linss & N. Madden
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 507
EP - 519
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/734.html
KW - Reaction-diffusion problems, layer-adapted meshes, alternating directions, singular perturbation.
AB - <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>