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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A sinc-collocation method for
initial value problems


Authors: Timothy S. Carlson, Jack Dockery and John Lund
Journal: Math. Comp. 66 (1997), 215-235
MSC (1991): Primary 65L05, 65L60
MathSciNet review: 1372000
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Abstract | References | Similar Articles | Additional Information

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

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00789-8
PII: S 0025-5718(97)00789-8
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.
Article copyright: © Copyright 1997 American Mathematical Society