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Volume 7, Issue 3
Shishkin Meshes in the Numerical Solution of Singularly Perturbed Differential Equations

N. Kopteva & E. O'Riordan

Int. J. Numer. Anal. Mod., 7 (2010), pp. 393-415.

Published online: 2010-07

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  • Abstract

This article reviews some of the salient features of the piecewise-uniform Shishkin mesh. The central analytical techniques involved in the associated numerical analysis are explained via a particular class of singularly perturbed differential equations. A detailed discussion of the Shishkin solution decomposition is included. The generality of the numerical approach introduced by Shishkin is highlighted. The impact of Shishkin's ideas on the field of singularly perturbed differential is assessed in this selective review of his research output over the past thirty years.

  • Keywords

Singularly perturbed problems, Shishkin mesh, Shishkin solution decomposition.

  • AMS Subject Headings

65N06, 65N12, 65N15, 65N50, 65L10, 65L11, 65L12, 65L20, 65L50, 35B25, 35C20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-393, author = {N. Kopteva and E. O'Riordan}, title = {Shishkin Meshes in the Numerical Solution of Singularly Perturbed Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {393--415}, abstract = {

This article reviews some of the salient features of the piecewise-uniform Shishkin mesh. The central analytical techniques involved in the associated numerical analysis are explained via a particular class of singularly perturbed differential equations. A detailed discussion of the Shishkin solution decomposition is included. The generality of the numerical approach introduced by Shishkin is highlighted. The impact of Shishkin's ideas on the field of singularly perturbed differential is assessed in this selective review of his research output over the past thirty years.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/727.html} }
TY - JOUR T1 - Shishkin Meshes in the Numerical Solution of Singularly Perturbed Differential Equations AU - N. Kopteva & E. O'Riordan JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 393 EP - 415 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/727.html KW - Singularly perturbed problems, Shishkin mesh, Shishkin solution decomposition. AB -

This article reviews some of the salient features of the piecewise-uniform Shishkin mesh. The central analytical techniques involved in the associated numerical analysis are explained via a particular class of singularly perturbed differential equations. A detailed discussion of the Shishkin solution decomposition is included. The generality of the numerical approach introduced by Shishkin is highlighted. The impact of Shishkin's ideas on the field of singularly perturbed differential is assessed in this selective review of his research output over the past thirty years.

N. Kopteva and E. O'Riordan. (2010). Shishkin Meshes in the Numerical Solution of Singularly Perturbed Differential Equations. International Journal of Numerical Analysis and Modeling. 7 (3). 393-415. doi:
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