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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.

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On the non-existence of $\epsilon$-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems
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by Paul A. Farrell, John J. H. Miller, Eugene O’Riordan and Grigorii I. Shishkin PDF
Math. Comp. 67 (1998), 603-617 Request permission


In this paper fitted finite difference methods on a uniform mesh with internodal spacing $h$, are considered for a singularly perturbed semilinear two-point boundary value problem. It is proved that a scheme of this type with a frozen fitting factor cannot converge $\varepsilon$-uniformly in the maximum norm to the solution of the differential equation as the mesh spacing $h$ goes to zero. Numerical experiments are presented which show that the same result is true for a number of schemes with variable fitting factors.
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Additional Information
  • Paul A. Farrell
  • Affiliation: Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242
  • Email:
  • John J. H. Miller
  • Affiliation: Department of Mathematics, Trinity College, Dublin 2, Ireland
  • Email:
  • Eugene O’Riordan
  • Affiliation: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
  • Email:
  • Grigorii I. Shishkin
  • Affiliation: Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia
  • Email:
  • Received by editor(s): July 3, 1995
  • Received by editor(s) in revised form: February 9, 1996
  • Additional Notes: Supported in part under NSF grant DMS-9627244.
    The first author was supported in part by the Research Council of Kent State University.
    The fourth author was supported in part by the Russian Foundation for Basic Research under Grant N 95-01-00039.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 603-617
  • MSC (1991): Primary 34B15, 65L12; Secondary 34L30, 65L10
  • DOI:
  • MathSciNet review: 1451321