106151 20230519145354.0 doi 10.1016/j.cam.2020.113020 sideral 118598 ART-2021-118598 eng Gracia, José Luis Universidad de Zaragoza (orcid)0000-0003-2538-9027 A finite difference method for an initial–boundary value problem with a Riemann–Liouville–Caputo spatial fractional derivative 2021 Access copy available to the general public Unrestricted An initial–boundary value problem with a Riemann–Liouville–Caputo space fractional derivative of order a¿(1, 2) is considered, where the boundary conditions are reflecting. A fractional Friedrichs’ inequality is derived and is used to prove that the problem approaches a steady-state solution when the source term is zero. The solution of the general problem is approximated using a finite difference scheme defined on a uniform mesh and the error analysis is given in detail for typical solutions which have a weak singularity near the spatial boundary x=0. It is proved that the scheme converges with first order in the maximum norm. Numerical results are given that corroborate our theoretical results for the order of convergence of the difference scheme, the approach of the solution to steady state, and mass conservation. info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 2.872 2021 MATHEMATICS, APPLIED 37 / 267 = 0.139 2021 Q1 T1 0.875 2021 Computational Mathematics 2021 Q2 Applied Mathematics 2021 Q2 5.1 2021 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Stynes, Martin 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 381 (2021), 113020 1-14 J. comput. appl. math. Journal of Computational and Applied Mathematics 0377-0427 1262431 http://zaguan.unizar.es/record/106151/files/texto_completo.pdf Postprint 1334728 http://zaguan.unizar.es/record/106151/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:106151 articulos driver 2023-05-18-13:30:23 ARTICLE