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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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High order methods for weakly singular integral equations with nonsmooth input functions
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by G. Monegato and L. Scuderi PDF
Math. Comp. 67 (1998), 1493-1515 Request permission

Abstract:

To solve one-dimensional linear weakly singular integral equations on bounded intervals, with input functions which may be smooth or not, we propose to introduce first a simple smoothing change of variable, and then to apply classical numerical methods such as product-integration and collocation based on global polynomial approximations. The advantage of this approach is that the order of the methods can be arbitrarily high and that the associated linear systems one has to solve are very well-conditioned.
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Additional Information
  • G. Monegato
  • Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
  • Email: monegato@polito.it
  • L. Scuderi
  • Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
  • Email: scuderi@polito.it
  • Received by editor(s): July 22, 1996
  • Additional Notes: This work was supported by the Ministero dell’Universitá e della Ricerca Scientifica e Tecnologica of Italy.

  • Dedicated: Dedicated to Professor M. R. Occorsio on the occasion of his 65th birthday
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 1493-1515
  • MSC (1991): Primary 65R20
  • DOI: https://doi.org/10.1090/S0025-5718-98-01005-9
  • MathSciNet review: 1604395