Numerical evaluation of the pth derivative of Jacobi series

Authors:
R. Barrio;J. M. Peña
Affiliations:
Grupo de Mecánica Espacial, University of Zaragoza, E-50009, Spain and Dpt. Matemática Aplicada, Edificio de Matemáticas, University of Zaragoza, E-50009 Zaragoza, Spain;Dpt. Matemática Aplicada, Edificio de Matemáticas, University of Zaragoza, E-50009 Zaragoza, Spain
Venue:
Applied Numerical Mathematics
Year:
2002

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Abstract

We introduce a new algorithm for the evaluation, at a general point x, of the pth derivative of a polynomial expressed as a finite series of Jacobi polynomials. The proposed algorithm permits the direct evaluation without obtaining the pth derivative of the polynomial itself, with the consequent memory and time savings. The stability of the algorithm is studied and it is compared with classical methods for evaluating derivatives in pseudospectral methods. Another algorithm, based on the previous one, is also proposed to reduce the rounding errors near the endpoints of the interval of evaluation.