Spectrum of the Jacobi Tau Approximation for the Second Derivative Operator

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Spectrum of the Jacobi Tau Approximation for the Second Derivative Operator

Abstract. It is proved that the eigenvalues of the Jacobi Tau method for the second derivative operator with Dirichlet boundary conditions are real, negative and distinct for a range of the Jacobi parameters. Special emphasis is placed on the symmetric case of the Gegenbauer Tau method where the range of parameters included in the theorems can be extended and characteristic polynomials given by...

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ژورنال

عنوان ژورنال: SIAM Journal on Numerical Analysis

سال: 2008

ISSN: 0036-1429,1095-7170

DOI: 10.1137/060665907