Sobolev orthogonal polynomials and spectral methods in boundary value problems Fernández Rodríguez, Lidia Marcellán, Francisco Pérez Fernández, Teresa Encarnación Piñar González, Miguel Ángel Jacobi polynomials Sobolev orthogonal polynomials Connection formulas Asymptotic properties Spectral methods and boundary value problems Fourier expansions The work by FM has been supported by FEDER/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación of Spain, grant PID2021-122154NB-I00, and the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors, grant EPUC3M23 in the context of the V PRICIT (Regional Program of Research and Technological Innovation). LF, TEP and MAP thanks Grant FQM-246-UGR20 funded by Consejería de Universidad, Investigación e Innovación and by European Union NextGenerationEU/PRTR; and Grant CEX2020-001105-M funded by MCIN/AEI/10.13039/501100011033. Funding for APC: Universidad Carlos III de Madrid (Agreement CRUE-Madroño 2023). 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. 2023-10-04T07:00:30Z 2023-10-04T07:00:30Z 2023-08 info:eu-repo/semantics/article L. Fernández, F. Marcellán, T.E. Pérez et al. Sobolev orthogonal polynomials and spectral methods in boundary value problems. Applied Numerical Mathematics. [https://doi.org/10.1016/j.apnum.2023.07.027] https://hdl.handle.net/10481/84814 10.1016/j.apnum.2023.07.027 eng http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Atribución 4.0 Internacional Elsevier