Analysis of an Alternating Direction Method Applied to Singularly Perturbed Reaction-Diffusion Problems
Year: 2010
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 507–519
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-734
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 507–519
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Reaction-diffusion problems layer-adapted meshes alternating directions singular perturbation.