TY - JOUR
T1 - Unconditional Convergence of Linearized TL1 Difference Methods for a Time-Fractional Coupled Nonlinear Schrödinger System
AU - Li , Min
AU - Li , Dongfang
AU - Ming , Ju
AU - Hendy , A. S.
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 1
EP - 30
PY - 2025
DA - 2025/04
SN - 18
DO - http://doi.org/10.4208/nmtma.OA-2024-0095
UR - https://global-sci.org/intro/article_detail/nmtma/23940.html
KW - Time-fractional coupled nonlinear Schrödinger system, transformed L1 schemes, unconditionally optimal error estimate, linearly implicit schemes.
AB - <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>