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Numerical implementation of the Sinc‐Galerkin method for second‐order hyperbolic equations
Author(s) -
McArthur Kelly M.,
Bowers Kenneth L.,
Lund John
Publication year - 1987
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690030303
Subject(s) - sinc function , mathematics , galerkin method , rate of convergence , discontinuous galerkin method , basis (linear algebra) , exponential function , basis function , convergence (economics) , order (exchange) , space (punctuation) , numerical analysis , mathematical analysis , finite element method , geometry , computer science , computer network , channel (broadcasting) , physics , finance , economics , thermodynamics , economic growth , operating system
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 2 N + 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.