000061717 001__ 61717
000061717 005__ 20190709135448.0
000061717 0247_ $$2doi$$a10.1137/16M1082329
000061717 0248_ $$2sideral$$a99223
000061717 037__ $$aART-2017-99223
000061717 041__ $$aeng
000061717 100__ $$aStynes, M.
000061717 245__ $$aError analysis of a finite difference method on graded meshes for a time-fractional diffusion equation
000061717 260__ $$c2017
000061717 5060_ $$aAccess copy available to the general public$$fUnrestricted
000061717 5203_ $$aA reaction-diffusion problem with a Caputo time derivative of order = 2 (0; 1) is considered. The solution of such a problem is shown in general to have a weak singularity near the initial time t = 0, and sharp point wise bounds on certain derivatives of this solution are derived. A new analysis of a standard finite difference method for the problem is given, taking into account this initial singularity. This analysis encompasses both uniform meshes and meshes that are graded in time, and includes new stability and consistency bounds. The final convergence result shows clearly how the regularity of the solution and the grading of the mesh affect the order of convergence of the difference scheme, so one can choose an optimal mesh grading. Numerical results are presented that confirm the sharpness of the error analysis.
000061717 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R
000061717 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000061717 590__ $$a2.047$$b2017
000061717 591__ $$aMATHEMATICS, APPLIED$$b26 / 252 = 0.103$$c2017$$dQ1$$eT1
000061717 592__ $$a2.657$$b2017
000061717 593__ $$aNumerical Analysis$$c2017$$dQ1
000061717 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000061717 700__ $$aO''Riordan, E.
000061717 700__ $$0(orcid)0000-0003-2538-9027$$aGracia, J.L.$$uUniversidad de Zaragoza
000061717 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000061717 773__ $$g55, 2 (2017), 1057-1079$$pSIAM j. numer. anal.$$tSIAM JOURNAL ON NUMERICAL ANALYSIS$$x0036-1429
000061717 8564_ $$s476874$$uhttps://zaguan.unizar.es/record/61717/files/texto_completo.pdf$$yVersión publicada
000061717 8564_ $$s72442$$uhttps://zaguan.unizar.es/record/61717/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000061717 909CO $$ooai:zaguan.unizar.es:61717$$particulos$$pdriver
000061717 951__ $$a2019-07-09-11:39:27
000061717 980__ $$aARTICLE