@Article{NMTMA-18-1,
author = {Li , MinLi , DongfangMing , Ju and Hendy , A. S.},
title = {Unconditional Convergence of Linearized TL1 Difference Methods for a Time-Fractional Coupled Nonlinear Schrödinger System},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2025},
volume = {18},
number = {1},
pages = {1--30},
abstract = {<p style="text-align: justify;">This paper presents a transformed L1 (TL1) finite difference method for
the time-fractional coupled nonlinear Schrödinger system. Unconditionally optimal $L^2$ error estimates of the fully discrete scheme are obtained. The convergence results indicate that the method has an order of $2$ in the spatial direction and an
order of $2 − α$ in the temporal direction. The error estimates hold without any
spatial-temporal stepsize restriction. Such convergence results are obtained by applying a novel discrete fractional Grönwall inequality and the corresponding Sobolev
embedding theorems. Numerical experiments for both two-dimensional and three-dimensional models are carried out to confirm our theoretical findings.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2024-0095},
url = {http://global-sci.org/intro/article_detail/nmtma/23940.html}
}