Error analysis of the L1 method on graded and uniform meshes for a\n fractional-derivative problem in two and three dimensions

2017/09/26 by Natalia Kopteva, Kopteva, Natalia · 4 citations
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1709.09136

openalex publication_date 2017/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An initial-boundary value problem with a Caputo time derivative of fractional\norder \α\∈(0,1) is considered, solutions of which typically exhibit a\nsingular behaviour at an initial time. For this problem, we give a simple\nframework for the analysis of the error of L1-type discretizations on graded\nand uniform temporal meshes in the L_\∞ and L₂ norms. This framework\nis employed in the analysis of both finite difference and finite element\nspatial discretiztions. Our theoretical findings are illustrated by numerical\nexperiments.\n

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