## Computational aspects of pseudospectral Laguerre approximations.(English)Zbl 0708.65072

Computations with Laguerre and Hermite polynomials lead to ill- conditioned algorithms and to underflow and overflow problems, even when the degree of the polynomials is low. In order to avoid these problems, the author introduces an interesting scaling function which limits these phenomena and allows, for instance, the determination of the zeros of $$L_ n^{(\alpha)}(x)$$ for large values of the degree n.
Reviewer: L.Gatteschi

### MSC:

 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 65D20 Computation of special functions and constants, construction of tables 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 34B05 Linear boundary value problems for ordinary differential equations
Full Text:

### References:

 [1] Canuto, C.; Hussaini, M.Y.; Quarteroni, A.; Zang, T.A., Spectral methods in fluid dynamics, (1988), Springer New York, Springer Series in Computational Physics · Zbl 0658.76001 [2] Coulaud, O.; Funaro, D.; Kavian, O., Laguerre spectral approximation of elliptic problems in exterior domains, Rept. no. 690, Proceedings of ICOSAHOM, (1989), IAN-CNR Pavia, Italy, Como, Italy [3] D. Funaro and O. Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite functions, Math. Comp. (to appear). · Zbl 0764.35007 [4] Gatteschi, L., Proprietá asintotiche di una funzione associata ai polinomi di Laguerre e loro utilizzazione al calcolo numerico degli zeri dei polinomi stessi, Atti accad. sci. Torino, 98, (1963-1964) · Zbl 0131.07102 [5] Gottlieb, D.; Orszag, S.A., Numerical analysis of spectral methods: theory and applications, CBMS regional conference series in applied mathematics, (1977), SIAM Philadelphia, PA · Zbl 0412.65058 [6] Maday, Y.; Pernaud-Thomas, B.; Vandeven, H., Une réhabilitation des méthodes de type Laguerre, Rech. Aérospat., 6, 353-375, (1985) · Zbl 0604.42026 [7] Mavriplis, C., Laguerre polynomials for infinite-domain spectral elements, J. comput. phys., 80, 480-488, (1989) · Zbl 0665.65066 [8] Szegö, G., Orthogonal polynomials, (1939), AMS New York · JFM 65.0286.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.