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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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A class of singularly perturbed semilinear differential equations with interior layers
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by P. A. Farrell, E. O’Riordan and G. I. Shishkin PDF
Math. Comp. 74 (2005), 1759-1776 Request permission

Abstract:

In this paper singularly perturbed semilinear differential equations with a discontinuous source term are examined. A numerical method is constructed for these problems which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented that validate the theoretical results.
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Additional Information
  • P. A. Farrell
  • Affiliation: Department of Computer Science, Kent State University, Kent, Ohio 44242, U.S.A.
  • Email: farrell@cs.kent.edu
  • E. O’Riordan
  • Affiliation: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
  • Email: eugene.oriordan@dcu.ie
  • G. I. Shishkin
  • Affiliation: Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia
  • Email: shishkin@imm.uran.ru
  • Received by editor(s): October 13, 2003
  • Received by editor(s) in revised form: June 11, 2004
  • Published electronically: June 7, 2005
  • Additional Notes: This research was supported in part by the Albert College Fellowship Scheme of Dublin City University, by the Enterprise Ireland grant SC–2000–070 and by the Russian Foundation for Basic Research under grant No. 04–01–00578.
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 74 (2005), 1759-1776
  • MSC (2000): Primary 65L70, 65L20, 65L10, 65L12
  • DOI: https://doi.org/10.1090/S0025-5718-05-01764-3
  • MathSciNet review: 2164095