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000061911 005__ 20210121114504.0
000061911 0247_ $$2doi$$a10.1515/fca-2015-0027
000061911 0248_ $$2sideral$$a100547
000061911 037__ $$aART-2015-100547
000061911 041__ $$aeng
000061911 100__ $$0(orcid)0000-0003-2538-9027$$aGracia Lozano, José Luis$$uUniversidad de Zaragoza
000061911 245__ $$aFormal consistency versus actual convergence rates of difference schemes for fractional-derivative boundary value problems
000061911 260__ $$c2015
000061911 5060_ $$aAccess copy available to the general public$$fUnrestricted
000061911 5203_ $$aFinite 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.
000061911 536__ $$9info:eu-repo/grantAgreement/ES/MEC/MTM2010-16917
000061911 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000061911 590__ $$a2.246$$b2015
000061911 591__ $$aMATHEMATICS$$b10 / 312 = 0.032$$c2015$$dQ1$$eT1
000061911 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b15 / 101 = 0.149$$c2015$$dQ1$$eT1
000061911 591__ $$aMATHEMATICS, APPLIED$$b9 / 254 = 0.035$$c2015$$dQ1$$eT1
000061911 592__ $$a1.551$$b2015
000061911 593__ $$aApplied Mathematics$$c2015$$dQ1
000061911 593__ $$aAnalysis$$c2015$$dQ1
000061911 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000061911 700__ $$aStynes, Martin
000061911 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000061911 773__ $$g18 (2015), 419-436$$pFract. Calc. Appl. Anal.$$tFractional Calculus and Applied Analysis$$x1311-0454
000061911 8564_ $$s668573$$uhttps://zaguan.unizar.es/record/61911/files/texto_completo.pdf$$yVersión publicada
000061911 8564_ $$s17845$$uhttps://zaguan.unizar.es/record/61911/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000061911 909CO $$ooai:zaguan.unizar.es:61911$$particulos$$pdriver
000061911 951__ $$a2021-01-21-10:53:45
000061911 980__ $$aARTICLE