TY - JOUR
T1 - Alikhanov Linearized Galerkin Finite Element Methods for Nonlinear Time-Fractional Schrödinger Equations
AU - Qin , Hongyu
AU - Wu , Fengyan
AU - Zhou , Boya
JO - Journal of Computational Mathematics
VL - 6
SP - 1305
EP - 1324
PY - 2023
DA - 2023/11
SN - 41
DO - http://doi.org/10.4208/jcm.2112-m2021-0113
UR - https://global-sci.org/intro/article_detail/jcm/22113.html
KW - Fractional Grönwall type inequality, Nonlinear time-fractional Schrödinger
equation, Error analysis.
AB - <p style="text-align: justify;">We present Alikhanov linearized Galerkin methods for solving the nonlinear time fractional Schrödinger equations. Unconditionally optimal estimates of the fully-discrete scheme are obtained by using the fractional time-spatial splitting argument. The convergence
results indicate that the error estimates hold without any spatial-temporal stepsize restrictions. Numerical experiments are done to verify the theoretical results.</p>