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Volume 41, Issue 6
Alikhanov Linearized Galerkin Finite Element Methods for Nonlinear Time-Fractional Schrödinger Equations

Hongyu Qin, Fengyan Wu & Boya Zhou

DOI: 10.4208/jcm.2112-m2021-0113

J. Comp. Math., 41 (2023), pp. 1305-1324.

Published online: 2023-11

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  • Abstract

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.

  • Keywords

Fractional Grönwall type inequality, Nonlinear time-fractional Schrödinger equation, Error analysis.

  • AMS Subject Headings

65M60, 65M12, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-41-1305, author = {Qin , HongyuWu , Fengyan and Zhou , Boya}, title = {Alikhanov Linearized Galerkin Finite Element Methods for Nonlinear Time-Fractional Schrödinger Equations}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {6}, pages = {1305--1324}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2112-m2021-0113}, url = {http://global-sci.org/intro/article_detail/jcm/22113.html} }
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 -

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.

Hongyu Qin, Fengyan Wu & Boya Zhou. (2023). Alikhanov Linearized Galerkin Finite Element Methods for Nonlinear Time-Fractional Schrödinger Equations. Journal of Computational Mathematics. 41 (6). 1305-1324. doi:10.4208/jcm.2112-m2021-0113
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