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Numerical implementation of the Sinc‐Galerkin method for second‐order hyperbolic equations

Numerical implementation of the Sinc‐Galerkin method for second‐order hyperbolic equations A fully Galerkin method in both space and time is developed for the second‐order, linear hyperbolic problem. Sinc basis functions are used and error bounds are given which show the exponential convergence rate of the method. The matrices necessary for the formulation of the discrete system are easily assembled. They require no numerical integrations (merely point evaluations) to be filled. The discrete problem is formulated in two different ways and solution techniques for each are described. Consideration of the two formulations is motivated by the computational architecture available. Each has advantages for the appropriate hardware. Numerical results reported show that if 2N + 1 basis functions are used then the exponential convergence rate \documentclass{article}\pagestyle{empty}\begin{document}$ 0\left({\exp \left({- \kappa \sqrt N} \right)} \right) $\end{document}, κ > 0, is attained for both analytic and singular problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerical Methods for Partial Differential Equations Wiley

Numerical implementation of the Sinc‐Galerkin method for second‐order hyperbolic equations

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References (6)

Publisher
Wiley
Copyright
Copyright © 1987 Wiley Periodicals, Inc.
ISSN
0749-159X
eISSN
1098-2426
DOI
10.1002/num.1690030303
Publisher site
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Abstract

A fully Galerkin method in both space and time is developed for the second‐order, linear hyperbolic problem. Sinc basis functions are used and error bounds are given which show the exponential convergence rate of the method. The matrices necessary for the formulation of the discrete system are easily assembled. They require no numerical integrations (merely point evaluations) to be filled. The discrete problem is formulated in two different ways and solution techniques for each are described. Consideration of the two formulations is motivated by the computational architecture available. Each has advantages for the appropriate hardware. Numerical results reported show that if 2N + 1 basis functions are used then the exponential convergence rate \documentclass{article}\pagestyle{empty}\begin{document}$ 0\left({\exp \left({- \kappa \sqrt N} \right)} \right) $\end{document}, κ > 0, is attained for both analytic and singular problems.

Journal

Numerical Methods for Partial Differential Equations – Wiley

Published: Sep 1, 1987

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