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Volume 7, Issue 3
Analysis of an Alternating Direction Method Applied to Singularly Perturbed Reaction-Diffusion Problems

T. Linss & N. Madden

Int. J. Numer. Anal. Mod., 7 (2010), pp. 507-519.

Published online: 2010-07

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  • 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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65N06

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-507, author = {}, 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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/734.html} }
TY - JOUR T1 - Analysis of an Alternating Direction Method Applied to Singularly Perturbed Reaction-Diffusion Problems 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 -

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.

T. Linss & N. Madden. (1970). Analysis of an Alternating Direction Method Applied to Singularly Perturbed Reaction-Diffusion Problems. International Journal of Numerical Analysis and Modeling. 7 (3). 507-519. doi:
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