Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation

Stynes, M. ; O''Riordan, E. ; Gracia, J.L. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1137/16M1082329

Año: 2017

Publicado en: SIAM JOURNAL ON NUMERICAL ANALYSIS 55, 2 (2017), 1057-1079
ISSN: 0036-1429

Factor impacto JCR: 2.047 (2017)

Categ. JCR: MATHEMATICS, APPLIED rank: 26 / 252 = 0.103 (2017) - Q1 - T1

Factor impacto SCIMAGO: 2.657 - Numerical Analysis (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)