Volume 5, Issue 4
Uniform Convergence via Preconditioning.

Zichen Deng

DOI:

Int. J. Numer. Anal. Mod. B,5 (2014), pp. 347-356

Published online: 2014-05

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  • Abstract

The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on the Shishkin mesh is analyzed. A new, conceptually simple proof of pointwise convergence uniform in the perturbation parameter is provided. The proof is based on the preconditioning of the discrete system.

  • Keywords

singular perturbation convection-diffusion boundary-value problem Shishkin mesh finite differences uniform convergence preconditioning

  • AMS Subject Headings

65L10 65L12 65L20 65L70

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COPYRIGHT: © Global Science Press

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@Article{IJNAMB-5-347, author = {Zichen Deng}, title = { Uniform Convergence via Preconditioning.}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2014}, volume = {5}, number = {4}, pages = {347--356}, abstract = {The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on the Shishkin mesh is analyzed. A new, conceptually simple proof of pointwise convergence uniform in the perturbation parameter is provided. The proof is based on the preconditioning of the discrete system.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/239.html} }
TY - JOUR T1 - Uniform Convergence via Preconditioning. AU - Zichen Deng JO - International Journal of Numerical Analysis Modeling Series B VL - 4 SP - 347 EP - 356 PY - 2014 DA - 2014/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/239.html KW - singular perturbation KW - convection-diffusion KW - boundary-value problem KW - Shishkin mesh KW - finite differences KW - uniform convergence KW - preconditioning AB - The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on the Shishkin mesh is analyzed. A new, conceptually simple proof of pointwise convergence uniform in the perturbation parameter is provided. The proof is based on the preconditioning of the discrete system.
Zichen Deng. (1970). Uniform Convergence via Preconditioning.. International Journal of Numerical Analysis Modeling Series B. 5 (4). 347-356. doi:
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