Unconditional Convergence of Linearized TL1 Difference Methods for a Time-Fractional Coupled Nonlinear Schrödinger System
Year: 2025
Author: Min Li, Dongfang Li, Ju Ming, A. S. Hendy
Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 1 : pp. 1–30
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2024-0095
Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 1 : pp. 1–30
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Time-fractional coupled nonlinear Schrödinger system transformed L1 schemes unconditionally optimal error estimate linearly implicit schemes.