61911 20210121114504.0 doi 10.1515/fca-2015-0027 sideral 100547 ART-2015-100547 eng (orcid)0000-0003-2538-9027 Gracia Lozano, José Luis Universidad de Zaragoza Formal consistency versus actual convergence rates of difference schemes for fractional-derivative boundary value problems 2015 Access copy available to the general public Unrestricted Finite difference methods for approximating fractional derivatives are often analyzed by determining their order of consistency when applied to smooth functions, but the relationship between this measure and their actual numerical performance is unclear. Thus in this paper several wellknown difference schemes are tested numerically on simple Riemann-Liouville and Caputo boundary value problems posed on the interval [0, 1] to determine their orders of convergence (in the discrete maximum norm) in two unexceptional cases: (i) when the solution of the boundary-value problem is a polynomial (ii) when the data of the boundary value problem is smooth. In many cases these tests reveal gaps between a method’s theoretical order of consistency and its actual order of convergence. In particular, numerical results show that the popular shifted Gr¨unwald-Letnikov scheme fails to converge for a Riemann-Liouville example with a polynomial solution p(x), and a rigorous proof is given that this scheme (and some other schemes) cannot yield a convergent solution when p(0)¿ 0. info:eu-repo/grantAgreement/ES/MEC/MTM2010-16917 info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 2.246 2015 MATHEMATICS 10 / 312 = 0.032 2015 Q1 T1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 15 / 101 = 0.149 2015 Q1 T1 MATHEMATICS, APPLIED 9 / 254 = 0.035 2015 Q1 T1 1.551 2015 Applied Mathematics 2015 Q1 Analysis 2015 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Stynes, Martin 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 18 (2015), 419-436 Fract. Calc. Appl. Anal. Fractional Calculus and Applied Analysis 1311-0454 668573 http://zaguan.unizar.es/record/61911/files/texto_completo.pdf Versión publicada 17845 http://zaguan.unizar.es/record/61911/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:61911 articulos driver 2021-01-21-10:53:45 ARTICLE