134982 20260217205545.0 doi 10.1007/s40314-024-02730-6 sideral 138495 ART-2024-138495 eng Gracia, José Luis Universidad de Zaragoza (orcid)0000-0003-2538-9027 A collocation method for an RLC fractional derivative two-point boundary value problem with a singular solution 2024 A two-point boundary value problem whose highest-order derivative is a Riemann–Liouville–Caputo derivative of order is considered. A similar problem was considered in Gracia et al. (BIT 60:411–439, 2020) but under a simplifying assumption that excluded singular solutions. In the present paper, this assumption is not imposed; furthermore, the finite difference method of the BIT paper, which was proved to attain 1st-order convergence under a sign restriction on the convective term, is replaced by a piecewise polynomial collocation method which can give any desired integer order of convergence on a suitably graded mesh. An error analysis of the collocation method is given which removes the above sign restriction and numerical results are presented to support our theoretical conclusions. The tools devised for this analysis include new comparison principles for Caputo initial-value problems and weakly singular Volterra integral equations that are of independent interest. Numerical experiments demonstrate the sharpness of our theoretical results. info:eu-repo/grantAgreement/ES/DGA/E24-23R info:eu-repo/grantAgreement/ES/MICINN/PID2022-137334NB-I00 info:eu-repo/grantAgreement/ES/MICINN/PID2022-141385NB-I00 info:eu-repo/semantics/closedAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 2.5 2024 MATHEMATICS, APPLIED 39 / 344 = 0.113 2024 Q1 T1 0.631 2024 Computational Mathematics 2024 Q2 Applied Mathematics 2024 Q2 4.2 2024 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Stynes, Martin 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 43, 199 (2024), [23 pp.] COMPUTATIONAL & APPLIED MATHEMATICS COMPUTATIONAL & APPLIED MATHEMATICS 2238-3603 616461 http://zaguan.unizar.es/record/134982/files/texto_completo.pdf Versión publicada 1302083 http://zaguan.unizar.es/record/134982/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:134982 articulos driver 2026-02-17-20:38:06 ARTICLE