000056087 001__ 56087
000056087 005__ 20210121114458.0
000056087 0247_ $$2doi$$a10.1515/cmam-2014-0024
000056087 0248_ $$2sideral$$a89299
000056087 037__ $$aART-2015-89299
000056087 041__ $$aeng
000056087 100__ $$aStynes, M.
000056087 245__ $$aBoundary layers in a two-point boundary value problem with a caputo fractional derivative
000056087 260__ $$c2015
000056087 5060_ $$aAccess copy available to the general public$$fUnrestricted
000056087 5203_ $$aA two-point boundary value problem is considered on the interval [0, 1], where the leading term in the differential operator is a Caputo fractional derivative of order ¿ with 1 < ¿ < 2. Writing ¿ for the solution of the problem, it is known that typically ¿¿¿(¿) blows up as ¿ ¿ 0. A numerical example demonstrates the possibility of a further phenomenon that imposes difficulties on numerical methods: ¿ may exhibit a boundary layer at ¿ = 1 when ¿ is near 1. The conditions on the data of the problem under which this layer appears are investigated by first solving the constant-coefficient case using Laplace transforms, determining precisely when a layer is present in this special case, then using this information to enlighten our examination of the general variable-coefficient case (in particular, in the construction of a barrier function for ¿). This analysis proves that usually no boundary layer can occur in the solution ¿ at ¿ = 0, and that the quantity ¿ = max¿¿[0,1] ¿(¿), where ¿ is the coefficient of the first-order term in the differential operator, is critical: when¿ < 1,noboundarylayerispresentwhen¿isnear1,butwhen¿ = 1thenaboundarylayerat¿ = 1 is possible. Numerical results illustrate the sharpness of most of our results.
000056087 536__ $$9info:eu-repo/grantAgreement/ES/MEC/MTM2010-16917
000056087 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000056087 590__ $$a0.673$$b2015
000056087 591__ $$aMATHEMATICS, APPLIED$$b163 / 254 = 0.642$$c2015$$dQ3$$eT2
000056087 592__ $$a0.901$$b2015
000056087 593__ $$aApplied Mathematics$$c2015$$dQ2
000056087 593__ $$aNumerical Analysis$$c2015$$dQ2
000056087 593__ $$aComputational Mathematics$$c2015$$dQ2
000056087 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000056087 700__ $$0(orcid)0000-0003-2538-9027$$aGracia, J.L.$$uUniversidad de Zaragoza
000056087 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000056087 773__ $$g15, 1 (2015), 79-95$$pComput. methods appl. math.$$tComputational Methods in Applied Mathematics$$x1609-4840
000056087 8564_ $$s687666$$uhttps://zaguan.unizar.es/record/56087/files/texto_completo.pdf$$yVersión publicada
000056087 8564_ $$s85645$$uhttps://zaguan.unizar.es/record/56087/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000056087 909CO $$ooai:zaguan.unizar.es:56087$$particulos$$pdriver
000056087 951__ $$a2021-01-21-10:49:46
000056087 980__ $$aARTICLE