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 - <p style="text-align: justify;">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.</p>