000134982 001__ 134982
000134982 005__ 20240509150149.0
000134982 0247_ $$2doi$$a10.1007/s40314-024-02730-6
000134982 0248_ $$2sideral$$a138495
000134982 037__ $$aART-2024-138495
000134982 041__ $$aeng
000134982 100__ $$0(orcid)0000-0003-2538-9027$$aGracia, José Luis$$uUniversidad de Zaragoza
000134982 245__ $$aA collocation method for an RLC fractional derivative two-point boundary value problem with a singular solution
000134982 260__ $$c2024
000134982 5203_ $$aA 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.
000134982 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-23R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-137334NB-I00$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-141385NB-I00
000134982 540__ $$9info:eu-repo/semantics/closedAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000134982 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000134982 700__ $$aStynes, Martin
000134982 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000134982 773__ $$g43, 199 (2024), [23 pp.]$$pCOMPUTATIONAL & APPLIED MATHEMATICS$$tCOMPUTATIONAL & APPLIED MATHEMATICS$$x2238-3603
000134982 8564_ $$s616461$$uhttps://zaguan.unizar.es/record/134982/files/texto_completo.pdf$$yVersión publicada
000134982 8564_ $$s1302083$$uhttps://zaguan.unizar.es/record/134982/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000134982 909CO $$ooai:zaguan.unizar.es:134982$$particulos$$pdriver
000134982 951__ $$a2024-05-09-13:06:40
000134982 980__ $$aARTICLE