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Spectral methods for periodic initial value problems with nonsmooth data

Authors: Pravir Dutt and A. K. Singh
Journal: Math. Comp. 61 (1993), 645-658
MSC: Primary 65M70
MathSciNet review: 1195431
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Abstract: In this paper we consider hyperbolic initial value problems subject to periodic boundary conditions with nonsmooth data. We show that if we filter the data and solve the problem by the Galerkin-Collocation method, recently proposed by us, then we can recover pointwise values with spectral accuracy, provided that the actual solution is piecewise smooth. For this we have to perform a local smoothing of the computed solution.

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Keywords: Discontinuous data, Galerkin-Collocation method, least squares solution, negative Sobolev norms, a priori energy estimates, local smoothing, spectral accuracy
Article copyright: © Copyright 1993 American Mathematical Society

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