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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem
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by Natalia Kopteva PDF
Math. Comp. 76 (2007), 631-646 Request permission


A semilinear reaction-diffusion equation with multiple solutions is considered in a smooth two-dimensional domain. Its diffusion parameter $\varepsilon ^2$ is arbitrarily small, which induces boundary layers. Constructing discrete sub- and super-solutions, we prove existence and investigate the accuracy of multiple discrete solutions on layer-adapted meshes of Bakhvalov and Shishkin types. It is shown that one gets second-order convergence (with, in the case of the Shishkin mesh, a logarithmic factor) in the discrete maximum norm, uniformly in $\varepsilon$ for $\varepsilon \le Ch$. Here $h>0$ is the maximum side length of mesh elements, while the number of mesh nodes does not exceed $Ch^{-2}$. Numerical experiments are performed to support the theoretical results.
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Additional Information
  • Natalia Kopteva
  • Affiliation: Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
  • MR Author ID: 610720
  • ORCID: 0000-0001-7477-6926
  • Email:
  • Received by editor(s): October 8, 2005
  • Received by editor(s) in revised form: February 23, 2006
  • Published electronically: December 27, 2006
  • Additional Notes: This publication has emanated from research conducted with the financial support of Science Foundation Ireland under the Basic Research Grant Programme 2004; Grant 04/BR/M0055.

  • Dedicated: Dedicated to Professor V. B. Andreev on the occasion of his 65th birthday
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 631-646
  • MSC (2000): Primary 65N06, 65N15, 65N30; Secondary 35B25
  • DOI:
  • MathSciNet review: 2291831