@Article{NMTMA-18-226,
author = {Liu , JunFu , HongfeiZhang , Bingyin and Zhang , Jiansong},
title = {Analysis and Efficient Implementation of Quadratic Spline Collocation ADI Methods for Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2025},
volume = {18},
number = {1},
pages = {226--258},
abstract = {<p style="text-align: justify;">In this paper, a quadratic spline collocation (QSC) method combined with $L1$ time discretization in the framework of alternating direction implicit (ADI) approach, namely ADI-QSC-$L$1 method, is developed to solve the variable-order time-fractional mobile-immobile diffusion equations in multi-dimensional spaces. Discrete $L_2$ norm-based stability and error estimate are carefully discussed, which
show that the proposed method is unconditionally stable and convergent with first-order accuracy in time and second-order accuracy in space. Then, based on the
exponential-sum-approximation technique for the fast evaluation of the variable-order Caputo fractional derivative, an efficient implementation strategy of the ADI-QSC-$L1$ method, named ADI-QSC-${\rm F}L1$ is presented, which further improves the
computational efficiency by reduced memory requirement and computational cost.
Finally, numerical examples are provided to support both the theoretical results and
efficiency of the developed method.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2024-0086},
url = {http://global-sci.org/intro/article_detail/nmtma/23948.html}
}