130787 20240131210811.0 doi 10.1007/s10543-019-00777-0 sideral 118663 ART-2020-118663 eng Gracia, José Luis Universidad de Zaragoza (orcid)0000-0003-2538-9027 Convergence analysis of a finite difference scheme for a two-point boundary value problem with a Riemann–Liouville–Caputo fractional derivative 2020 The Riemann–Liouville–Caputo (RLC) derivative is a new class of derivative that is motivated by modelling considerations; it lies between the more familiar Riemann–Liouville and Caputo derivatives. The present paper studies a two-point boundary value problem on the interval [0,  L] whose highest-order derivative is an RLC derivative of order a¿ (1 , 2). It is shown that the choice of boundary condition at x= 0 strongly influences the regularity of the solution. For the case where the solution lies in C1[0 , L] n Cq + 1(0 , L] for some positive integer q, a finite difference scheme is used to solve the problem numerically on a uniform mesh. In the error analysis of the scheme, the weakly singular behaviour of the solution at x= 0 is taken into account and it is shown that the method is almost first-order convergent. Numerical results are presented to illustrate the performance of the method. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R info:eu-repo/grantAgreement/ES/MCYT-FEDER/MTM2016-75139-R info:eu-repo/grantAgreement/ES/MINECO/MTM2016-75139-R info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.663 2020 MATHEMATICS, APPLIED 102 / 265 = 0.385 2020 Q2 T2 COMPUTER SCIENCE, SOFTWARE ENGINEERING 64 / 108 = 0.593 2020 Q3 T2 0.904 2020 Applied Mathematics 2020 Q1 Software 2020 Q1 Computer Networks and Communications 2020 Q1 Computational Mathematics 2020 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion O’Riordan, Eugene Stynes, Martin 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 60, 2 (2020), 411-439 BIT BIT Numerical Mathematics 0006-3835 271806 http://zaguan.unizar.es/record/130787/files/texto_completo.pdf Postprint 1342859 http://zaguan.unizar.es/record/130787/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:130787 articulos driver 2024-01-31-19:21:05 ARTICLE