61717 20190709135448.0 doi 10.1137/16M1082329 sideral 99223 ART-2017-99223 eng Stynes, M. Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation 2017 Access copy available to the general public Unrestricted A 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. info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 2.047 2017 MATHEMATICS, APPLIED 26 / 252 = 0.103 2017 Q1 T1 2.657 2017 Numerical Analysis 2017 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion O''Riordan, E. (orcid)0000-0003-2538-9027 Gracia, J.L. Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 55, 2 (2017), 1057-1079 SIAM j. numer. anal. SIAM JOURNAL ON NUMERICAL ANALYSIS 0036-1429 476874 http://zaguan.unizar.es/record/61717/files/texto_completo.pdf Versión publicada 72442 http://zaguan.unizar.es/record/61717/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:61717 articulos driver 2019-07-09-11:39:27 ARTICLE