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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.

  • Keywords

Reaction-diffusion problems, layer-adapted meshes, alternating directions, singular perturbation.

  • AMS Subject Headings

65N06

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@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 = {

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 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 -

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 and N. Madden. (2010). 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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