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

DOI:
https://doi.org/10.1090/S0025-5718-97-00789-8

MathSciNet review:
1372000

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Abstract | References | Similar Articles | Additional Information

Abstract: A collocation procedure is developed for the initial value problem , , using the globally defined sinc basis functions. It is shown that this sinc procedure converges to the solution at an exponential rate, i.e., where and basis functions are used in the expansion. Problems on the domains and are used to illustrate the implementation and accuracy of the procedure.

**1.**B. Bialecki,*Sinc-collocation methods for two-point boundary value problems*, IMA J. Numer. Anal.**11**(1991), 357-375. MR**92f:65086****2.**T. S. Carlson,*Sinc methods for Burgers' equation*, Ph.D. thesis, Montana State University, 1995.**3.**N. Eggert, M. Jarratt, and J. Lund,*Sinc function computation of the eigenvalues of Sturm-Liouville problems*, J. Comput. Phys.**69**(1987), no. 1, 209-229. MR**89c:65090****4.**U. Grenander and G. Szegö,*Toeplitz forms and their applications*, 2nd ed., Chelsea Publishing Co., New York, 1984. MR**88b:42031****5.**J. Lund and K. L. Bowers,*Sinc methods for quadrature and differential equations*, SIAM, Philadelphia, 1992. MR**93i:65004****6.**J. Lund and B. V. Riley,*A sinc-collocation method for the computation of the eigenvalues of the radial Schrödinger equation*, IMA J. Numer. Anal.**4**(1984), 83-98. MR**86f:65134****7.**L. Lundin and F. Stenger,*Cardinal type approximations of a function and its derivatives*, SIAM J. Math. Anal.**10**(1979), 139-160. MR**81c:41043****8.**K. M. McArthur,*A collocative variation of the Sinc-Galerkin method for second order boundary value problems*, Computation and Control (K. Bowers and J. Lund, eds.), Birkhäuser, Boston, 1989, pp. 253-261. CMP**90:10****9.**A. C. Morlet,*Convergence of the sinc method for a fourth-order ordinary differential equation with an application*, SIAM J. Numer. Anal.**32**(1995), 1475-1503. MR**96f:65097****10.**F. Stenger,*Numerical methods based on sinc and analytic functions*, Springer-Verlag, New York, 1993. MR**94k:65003****11.**F. Stenger, B. Barkey, and R. Vakili,*Sinc convolution approximate solution of Burgers' equation*, Computation and Control III (K. Bowers and J. Lund, eds.), Birkhäuser, Boston, 1993, pp. 341-354. CMP**94:04**

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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:
https://doi.org/10.1090/S0025-5718-97-00789-8

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