Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=45303#.VL3_FSzQrzE Author(s) Jue Wang 1* , Fabian Waleffe 2 Affiliation(s) 1 Department of Mathematics, Union College, Schenectady, USA . 2 Department of Mathematics, University of Wisconsin-Madison, Madison, USA . ABSTRACT We complete and extend the asymptotic analysis of the spectrum of Jacobi Tau approximations that were first considered by Dubiner. The asymptotic formulas for Jacobi polynomials PN(α ,β ) ,α ,β > ?1 are derived and confirmed by numerical approximations. More accurate results for the slowest decaying mode are obtained. We explain where the large negative eigenvalues come from. Furthermore, we show that a large negative eigenvalue of order ???? appears for ?1 <α < 0 ; there are no large negative eigenvalues for collocations at Gauss-Lobatto points. The asymptotic results indicate unstable eigenvalues for α >...
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