Technical Report CS0837

TR#:CS0837
Class:CS
Title: REMARKS ON THE FOURIER- GEGENBAUER METHOD.
Authors: L. Vozovoi, M. Israeli and A. Averbuch
PDFCS0837.pdf
Abstract: In this paper we investigate some numerical aspects of the Fourier-Gegenbauer method introduced in [1]. The asymptotic behavior of the Gegenbauer series is analyzed as well as the behavior of this series with small and moderate numbers of terms. A new criteria for obtaining an exponentially small truncation error is found. It is shown that the exponential convergence takes place only for the short-term Gegenbauer expansion. The computed Fourier-Gegenbauer expansion with a large number of terms exhibits the Gibbs phenomenon in spite of the fact that both the resolution and the truncation errors are exponentially small.
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