@Article{NMTMA-12-3,
author = {},
title = {Finite Difference Schemes for the Variable Coefficients Single and Multi-Term Time-Fractional Diffusion Equations with Non-Smooth Solutions on Graded and Uniform Meshes},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2019},
volume = {12},
number = {3},
pages = {845--866},
abstract = {<p style="text-align: justify;">Finite difference scheme for the variable coefficients subdiffusion equations
with non-smooth solutions is constructed and analyzed. The spatial derivative is discretized on a uniform mesh, and $L$1 approximation is used for the discretization of the
fractional time derivative on a possibly graded mesh. Stability of the proposed scheme
is given using the discrete energy method. The numerical scheme is $\mathcal{O}$ ($N$<sup>−min{2−$α$,$rα$}</sup>)
accurate in time, where $α$ (0 &lt; $α$ &lt; 1) is the order of the fractional time derivative, $r$ is an index of the mesh partition, and it is second order accurate in space. Extension to
multi-term time-fractional problems with nonhomogeneous boundary conditions is also
discussed, with the stability and error estimate proved both in the discrete $l$<sup>2</sup>-norm and
the $l$<sup>∞</sup>-norm on the nonuniform temporal mesh. Numerical results are given for both
the two-dimensional single and multi-term time-fractional equations.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2018-0046},
url = {https://global-sci.com/article/90421/finite-difference-schemes-for-the-variable-coefficients-single-and-multi-term-time-fractional-diffusion-equations-with-non-smooth-solutions-on-graded-and-uniform-meshes}
}