An Alternative Finite Difference Stability Analysis for a Multiterm Time-Fractional Initial-Boundary Value Problem
Year: 2020
Author: Xiaohui Liu, Martin Stynes
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 3 : pp. 427–436
Abstract
A fractional initial-boundary value problem is considered, where the differential operator includes a sum of Caputo temporal derivatives, and the solution has a weak singularity at the initial time $t$ = 0. The problem is solved numerically by a finite difference method based on applying the L1 method to discretise each temporal derivative on a graded mesh. Stability of this method is proved by generalising the analysis of Stynes $et$ $al$., SIAM J. Numer. Anal. 55 (2017), where the case of a single temporal derivative was investigated. This stability result is used to prove a sharp error estimate for the finite difference method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.010120.090320
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 3 : pp. 427–436
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Multiterm time-fractional initial-boundary value problem graded mesh L1 scheme discrete stability.
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