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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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On best possible order of convergence estimates in the collocation method and Galerkin’s method for singularly perturbed boundary value problems for systems of first-order ordinary differential equations
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by I. A. Blatov and V. V. Strygin PDF
Math. Comp. 68 (1999), 683-715 Request permission

Abstract:

The collocation method and Galerkin method using parabolic splines are considered. Special adaptive meshes whose number of knots is independent of the small parameter of the problem are used. Unimprovable estimates in the $L_\infty$-norm are obtained. For the Galerkin method these estimates are quasioptimal, while for the collocation method they are suboptimal.
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Additional Information
  • I. A. Blatov
  • Affiliation: Department of Applied Mathematics and Mechanics, Voronezh State University, Universitetskaya pl.1, Voronezh, Russia, 394693
  • Email: blatov@kvm.vsu.ru
  • V. V. Strygin
  • Affiliation: Department of Applied Mathematics and Mechanics, Voronezh State University, Universitetskaya pl.1, Voronezh, Russia, 394693
  • Email: strygin@kvm.vsu.ru
  • Received by editor(s): May 28, 1994
  • Received by editor(s) in revised form: February 11, 1995, and May 26, 1996
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 68 (1999), 683-715
  • MSC (1991): Primary 65-02, 65L99; Secondary 65G99, 45A10
  • DOI: https://doi.org/10.1090/S0025-5718-99-01034-0
  • MathSciNet review: 1620211