000130755 001__ 130755 000130755 005__ 20240131210810.0 000130755 0247_ $$2doi$$a10.1007/s10915-017-0631-4 000130755 0248_ $$2sideral$$a103776 000130755 037__ $$aART-2018-103776 000130755 041__ $$aeng 000130755 100__ $$0(orcid)0000-0003-2538-9027$$aGracia Lozano, José Luis$$uUniversidad de Zaragoza 000130755 245__ $$aA fitted scheme for a Caputo initial-boundary value problem 000130755 260__ $$c2018 000130755 5060_ $$aAccess copy available to the general public$$fUnrestricted 000130755 5203_ $$aIn this paper we consider an initial-boundary value problem with a Caputo time derivative of order (Formula presented.). The solution typically exhibits a weak singularity near the initial time and this causes a reduction in the orders of convergence of standard schemes. To deal with this singularity, the solution is computed with a fitted difference scheme on a graded mesh. The convergence of this scheme is analysed using a discrete maximum principle and carefully chosen barrier functions. Sharp error estimates are proved, which show an enhancement in the convergence rate compared with the standard L1 approximation on uniform meshes, and also indicate an optimal choice for the mesh grading. This optimal mesh grading is less severe than the optimal grading for the standard L1 scheme. Furthermore, the dependence of the error on the final time forms part of our error estimate. Numerical experiments are presented which corroborate our theoretical results. 000130755 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R 000130755 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000130755 590__ $$a2.37$$b2018 000130755 591__ $$aMATHEMATICS, APPLIED$$b26 / 254 = 0.102$$c2018$$dQ1$$eT1 000130755 592__ $$a1.434$$b2018 000130755 593__ $$aApplied Mathematics$$c2018$$dQ1 000130755 593__ $$aEngineering (miscellaneous)$$c2018$$dQ1 000130755 593__ $$aComputational Mathematics$$c2018$$dQ1 000130755 593__ $$aTheoretical Computer Science$$c2018$$dQ1 000130755 593__ $$aNumerical Analysis$$c2018$$dQ1 000130755 593__ $$aSoftware$$c2018$$dQ1 000130755 593__ $$aComputational Theory and Mathematics$$c2018$$dQ1 000130755 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000130755 700__ $$aO'Riordan, Eugene 000130755 700__ $$aStynes, Martin 000130755 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000130755 773__ $$g76, 1 (2018), 583–609$$pJ. sci. comput.$$tJournal of Scientific Computing$$x0885-7474 000130755 8564_ $$s332568$$uhttps://zaguan.unizar.es/record/130755/files/texto_completo.pdf$$yPostprint 000130755 8564_ $$s1127285$$uhttps://zaguan.unizar.es/record/130755/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000130755 909CO $$ooai:zaguan.unizar.es:130755$$particulos$$pdriver 000130755 951__ $$a2024-01-31-19:18:11 000130755 980__ $$aARTICLE