Volume 11, Issue 1
A Compact Difference Scheme for Time-Fractional Dirichlet Biharmonic Equation on Temporal Graded Meshes

Mingrong Cui

East Asian J. Appl. Math., 11 (2021), pp. 164-180.

Published online: 2020-11

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  • Abstract

The stability of a compact finite difference scheme on general nonuniform temporal meshes for a time fractional two-dimensional biharmonic problem is proved and graded mesh error estimates are derived. By using the Stephenson scheme for spatial derivatives discretisation, we simultaneously obtain approximate values of the gradient without any loss of accuracy. The discretisation of the Caputo derivative on graded meshes leads to a fully discrete implicit scheme. Numerical experiments support the theoretical findings and indicate that for problems with nonsmooth solutions, graded meshes have an advantage for very coarse temporal meshes.

  • Keywords

Fractional biharmonic equation, nonsmooth solution, graded mesh, compact difference scheme, stability and convergence.

  • AMS Subject Headings

65M06, 65M12, 65M15, 65N06, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-164, author = {Mingrong and Cui and and 9668 and and Mingrong Cui}, title = {A Compact Difference Scheme for Time-Fractional Dirichlet Biharmonic Equation on Temporal Graded Meshes}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {11}, number = {1}, pages = {164--180}, abstract = {

The stability of a compact finite difference scheme on general nonuniform temporal meshes for a time fractional two-dimensional biharmonic problem is proved and graded mesh error estimates are derived. By using the Stephenson scheme for spatial derivatives discretisation, we simultaneously obtain approximate values of the gradient without any loss of accuracy. The discretisation of the Caputo derivative on graded meshes leads to a fully discrete implicit scheme. Numerical experiments support the theoretical findings and indicate that for problems with nonsmooth solutions, graded meshes have an advantage for very coarse temporal meshes.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.270520.210920}, url = {http://global-sci.org/intro/article_detail/eajam/18418.html} }
TY - JOUR T1 - A Compact Difference Scheme for Time-Fractional Dirichlet Biharmonic Equation on Temporal Graded Meshes AU - Cui , Mingrong JO - East Asian Journal on Applied Mathematics VL - 1 SP - 164 EP - 180 PY - 2020 DA - 2020/11 SN - 11 DO - http://doi.org/10.4208/eajam.270520.210920 UR - https://global-sci.org/intro/article_detail/eajam/18418.html KW - Fractional biharmonic equation, nonsmooth solution, graded mesh, compact difference scheme, stability and convergence. AB -

The stability of a compact finite difference scheme on general nonuniform temporal meshes for a time fractional two-dimensional biharmonic problem is proved and graded mesh error estimates are derived. By using the Stephenson scheme for spatial derivatives discretisation, we simultaneously obtain approximate values of the gradient without any loss of accuracy. The discretisation of the Caputo derivative on graded meshes leads to a fully discrete implicit scheme. Numerical experiments support the theoretical findings and indicate that for problems with nonsmooth solutions, graded meshes have an advantage for very coarse temporal meshes.

Mingrong Cui. (2020). A Compact Difference Scheme for Time-Fractional Dirichlet Biharmonic Equation on Temporal Graded Meshes. East Asian Journal on Applied Mathematics. 11 (1). 164-180. doi:10.4208/eajam.270520.210920
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