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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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A sinc-collocation method for initial value problems
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by Timothy S. Carlson, Jack Dockery and John Lund PDF
Math. Comp. 66 (1997), 215-235 Request permission


A collocation procedure is developed for the initial value problem $u’(t) = f(t,u(t))$, $u(0) = 0$, using the globally defined sinc basis functions. It is shown that this sinc procedure converges to the solution at an exponential rate, i.e., $\mathcal { O} (M^{2} \exp (-\kappa \sqrt {M}) )$ where $\kappa > 0$ and $2M$ basis functions are used in the expansion. Problems on the domains $\mathbb {R} = (-\infty ,\infty )$ and $\mathbb {R} ^{+} = (0,\infty )$ are used to illustrate the implementation and accuracy of the procedure.
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Additional Information
  • Timothy S. Carlson
  • Affiliation: Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501
  • Email:
  • Jack Dockery
  • Affiliation: Department of Mathematics, Montana State University, Bozeman, Montana 59717
  • Email:
  • John Lund
  • Affiliation: Department of Mathematics, Montana State University, Bozeman, Montana 59717
  • Email:
  • Received by editor(s): February 27, 1995
  • Received by editor(s) in revised form: November 2, 1995, and January 26, 1996
  • Additional Notes: The first author was supported in part by the Office of Naval Research under contract ONR-00014-89-J-1114.
    The second author was supported in part by the National Science Foundation grants OSR-93-50-546 and DMS-94-04-160.
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 215-235
  • MSC (1991): Primary 65L05, 65L60
  • DOI:
  • MathSciNet review: 1372000