@Article{IJNAM-12-2,
author = {},
title = {Improved Error Estimates of a Finite Difference/Spectral Method for Time-Fractional  Diffusion Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2015},
volume = {12},
number = {2},
pages = {384--400},
abstract = {<p style="text-align: justify;">In this paper, we first consider the numerical method that Lin and Xu proposed and
analyzed in [Finite difference/spectral approximations for the time-fractional diffusion equation,
JCP 2007] for the time-fractional diffusion equation. It is a method based on the combination
of a finite different scheme in time and spectral method in space. The numerical analysis carried
out in that paper showed that the scheme is of $(2-\alpha)$-order convergence in time and spectral
accuracy in space for smooth solutions, where $\alpha$ is the time-fractional derivative order. The main
purpose of this paper consists in refining the analysis and providing a sharper estimate for both
time and space errors. More precisely, we improve the error estimates by giving a more accurate
coefficient in the time error term and removing the factor in the space error term, which grows
with decreasing time step. Then the theoretical results are validated by a number of numerical
tests.</p>},
issn = {2617-8710},
doi = {https://doi.org/2015-IJNAM-495},
url = {https://global-sci.com/article/83299/improved-error-estimates-of-a-finite-differencespectral-method-for-time-fractional-diffusion-equations}
}