TY - JOUR
T1 - An Alternative Finite Difference Stability Analysis for a Multiterm Time-Fractional Initial-Boundary Value Problem
AU - Liu , Xiaohui
AU - Stynes , Martin
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 427
EP - 436
PY - 2020
DA - 2020/06
SN - 10
DO - http://doi.org/10.4208/eajam.010120.090320
UR - https://global-sci.org/intro/article_detail/eajam/16975.html
KW - Multiterm time-fractional initial-boundary value problem, graded mesh, L1 scheme,
discrete stability.
AB - <p style="text-align: justify;">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.</p>