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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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Nyström-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels
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by Sheon-Young Kang, Israel Koltracht and George Rawitscher PDF
Math. Comp. 72 (2003), 729-756 Request permission

Abstract:

A new highly accurate numerical approximation scheme based on a Gauss type Clenshaw-Curtis quadrature for Fredholm integral equations of the second kind \[ x(t)+\int ^{b}_{a}k(t,s)x(s)ds=y(t),\] whose kernel $k(t,s)$ is either discontinuous or not smooth along the main diagonal, is presented. This scheme is of spectral accuracy when $k(t,s)$ is infinitely differentiable away from the diagonal $t = s$. Relation to the singular value decomposition is indicated. Application to integro-differential Schrödinger equations with nonlocal potentials is given.
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Additional Information
  • Sheon-Young Kang
  • Affiliation: Department of Mathematics, Purdue University North Central, Westville, Indiana 46391
  • Email: skang@purduenc.edu
  • Israel Koltracht
  • Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
  • Email: kolt@math.uconn.edu
  • George Rawitscher
  • Affiliation: Department of Physics, University of Connecticut, Storrs, Connecticut 06269
  • Email: rawitsch@uconnvm.uconn.edu
  • Received by editor(s): March 29, 2001
  • Received by editor(s) in revised form: July 9, 2001
  • Published electronically: March 8, 2002
  • Additional Notes: The work of the first author is partially supported by a fellowship from alumni of Mathematics Department, Chungnam National University, Korea.
  • © Copyright 2002 American Mathematical Society
  • Journal: Math. Comp. 72 (2003), 729-756
  • MSC (2000): Primary 45B05, 45J05, 65Rxx, 65R20, 81U10
  • DOI: https://doi.org/10.1090/S0025-5718-02-01431-X
  • MathSciNet review: 1954965