Abstract
In this paper we develop the Sinc-Galerkin collocation method for approximating the solution of initial boundary value problems for the heat equation in a finite space-time cylinder. One important feature of the Sinc method is that a uniform exponential error bound of the form O(e −c/h), where h is a step size, is typical for boundary data that is piecewise holomorphic with discontinuities at finitely many isolated values of t. This is allowed by calculating solutions in finite time intervals, which appears to be a new result and includes calculation of solutions that blow up at infinity or within finite time. The case of a finite time interval requires some care in evaluating the resulting inner products to obtain a sufficiently well-conditioned finite dimensional system of equations arising from discretization.
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References
D.L. LEWIS, J. LUND and K. L. BOWERS, “The Space-time Sinc-Galerkin Method for Parabolic Problems,” Internat. J. Numer. Methods Engrg. ,v. 24, 1987, pp 1629–1644.
J. LUND, “Symmetrization of the Sinc-Galerkin Method for Boundary Value Problems,” Math. Comp. ,v. 47, 1986, pp. 571–588.
J. LUND and K. L. BOWERS, Sinc Methods for Quadrature and Differential Equations ,SIAM, Philadelphia, PA, 1992.
F. STENGER, “Approximations via Whittakers Cardinal Function,” J. Approx. Theory ,v. 17, 1976, pp. 222–240.
F. STENGER, “Numerical Methods Based on Whittaker Cardinal, or Sinc Functions,” SIAM Rev. ,v. 23, 1981, 165–224.
M. STROMBERG,“Sinc Approximate Solution of Quasilinear Equations of Conservation Law Type,” Computation and Control ,Birkhäuser Boston, 1989, pp. 317–331.
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© 1993 Springer Science+Business Media New York
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Stromberg, M., Gilliam, X.L. (1993). Sinc-Galerkin Collocation Method for Parabolic Equations in Finite Space-Time Regions. In: Bowers, K., Lund, J. (eds) Computation and Control III. Progress in Systems and Control Theory, vol 15. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0321-6_26
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DOI: https://doi.org/10.1007/978-1-4612-0321-6_26
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6706-5
Online ISBN: 978-1-4612-0321-6
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