Volume 10, Issue 3
An Alternative Finite Difference Stability Analysis for a Multiterm Time-Fractional Initial-Boundary Value Problem

Xiaohui Liu & Martin Stynes

East Asian J. Appl. Math., 10 (2020), pp. 427-436.

Published online: 2020-06

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  • 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.

  • Keywords

Multiterm time-fractional initial-boundary value problem, graded mesh, L1 scheme, discrete stability.

  • AMS Subject Headings

65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-427, author = {Xiaohui Liu , and Martin Stynes , }, title = {An Alternative Finite Difference Stability Analysis for a Multiterm Time-Fractional Initial-Boundary Value Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.010120.090320}, url = {http://global-sci.org/intro/article_detail/eajam/16975.html} }
TY - JOUR T1 - An Alternative Finite Difference Stability Analysis for a Multiterm Time-Fractional Initial-Boundary Value Problem AU - Xiaohui Liu , AU - Martin Stynes , JO - East Asian Journal on Applied Mathematics VL - 3 SP - 427 EP - 436 PY - 2020 DA - 2020/06 SN - 10 DO - http://dor.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.

Xiaohui Liu & Martin Stynes. (2020). An Alternative Finite Difference Stability Analysis for a Multiterm Time-Fractional Initial-Boundary Value Problem. East Asian Journal on Applied Mathematics. 10 (3). 427-436. doi:10.4208/eajam.010120.090320
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