@misc{10481/84814,
year = {2023},
month = {8},
url = {https://hdl.handle.net/10481/84814},
abstract = {In the variational formulation of a boundary value problem for the harmonic oscillator, Sobolev inner products appear in a natural way. First, we study the sequences of Sobolev orthogonal polynomials with respect to such an inner product. Second, their representations in terms of a sequence of Gegenbauer polynomials are deduced as well as an algorithm to generate them in a recursive way is stated. The outer relative asymptotics between the Sobolev orthogonal polynomials and classical Legendre polynomials is obtained. Next we analyze the solution of the boundary value problem in terms of a Fourier-Sobolev projector. Finally, we provide numerical tests concerning the reliability and accuracy of the Sobolev spectral method.},
organization = {FEDER/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación of Spain PID2021-122154NB-I00},
organization = {Madrid Government   EPUC3M23},
organization = {Consejería de Universidad, Investigación e Innovación  FQM-246-UGR20},
organization = {European Union NextGenerationEU/PRTR},
organization = {MCIN/AEI/10.13039/501100011033:  CEX2020-001105-M},
organization = {Universidad Carlos III de Madrid CRUE-Madroño 2023},
publisher = {Elsevier},
keywords = {Jacobi polynomials},
keywords = {Sobolev orthogonal polynomials},
keywords = {Connection formulas},
keywords = {Asymptotic properties},
keywords = {Spectral methods and boundary value problems},
keywords = {Fourier expansions},
title = {Sobolev orthogonal polynomials and spectral methods in boundary value problems},
doi = {10.1016/j.apnum.2023.07.027},
author = {Fernández Rodríguez, Lidia and Marcellán, Francisco and Pérez Fernández, Teresa Encarnación and Piñar González, Miguel Ángel},
}