130755 20240131210810.0 doi 10.1007/s10915-017-0631-4 sideral 103776 ART-2018-103776 eng Gracia Lozano, José Luis Universidad de Zaragoza (orcid)0000-0003-2538-9027 A fitted scheme for a Caputo initial-boundary value problem 2018 In 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. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 2.37 2018 MATHEMATICS, APPLIED 26 / 254 = 0.102 2018 Q1 T1 1.434 2018 Applied Mathematics 2018 Q1 Engineering (miscellaneous) 2018 Q1 Computational Mathematics 2018 Q1 Theoretical Computer Science 2018 Q1 Numerical Analysis 2018 Q1 Software 2018 Q1 Computational Theory and Mathematics 2018 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion O'Riordan, Eugene Stynes, Martin 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 76, 1 (2018), 583–609 J. sci. comput. Journal of Scientific Computing 0885-7474 332568 http://zaguan.unizar.es/record/130755/files/texto_completo.pdf Postprint 1127285 http://zaguan.unizar.es/record/130755/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:130755 articulos driver 2024-01-31-19:18:11 ARTICLE