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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 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

Abstract:

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: tim@santafe.edu
  • Jack Dockery
  • Affiliation: Department of Mathematics, Montana State University, Bozeman, Montana 59717
  • Email: umsfjdoc@math.montana.edu
  • John Lund
  • Affiliation: Department of Mathematics, Montana State University, Bozeman, Montana 59717
  • Email: umsfjlun@math.montana.edu
  • 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: https://doi.org/10.1090/S0025-5718-97-00789-8
  • MathSciNet review: 1372000