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 -

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.