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On the Exponential Convergence of Spline Approximation Methods for Wiener-Hopf Equations

โœ Scribed by Johannes Elschner

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
542 KB
Volume
160
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Abstract

We consider the approximate solution of Wienerโ€Hopf integral equations by Galerkin, collocation and Nystrรถm methods based on piecewise polynomials where accuracy is achieved by increasing simultaneously the number of mesh points and the degree of the polynomials. We look for the stability of those methods in the L~q~ norm, 1โ‰คqโ‰คโˆž. Provided the exact solution is analytic on the halfโ€axis and decays exponentially at infinity, we prove an exponential rate of convergence with respect to the number of degrees of freedom.

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