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A Spatially Sixth-Order Hybrid L1-CCD Method for Solving Time Fractional Schrödinger Equations

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Abstract

We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an L1 strategy is employed for approximating the Caputo fractional derivative in the temporal direction, compact CCD finite difference approaches are incorporated in the space. A highly effective hybrid L1-CCD method is implemented successfully. The accuracy of this linearized scheme is order six in space, and order 2 − γ in time, where 0 < γ < 1 is the order of the Caputo fractional derivative involved. It is proved rigorously that the hybrid numerical method accomplished is unconditionally stable in the Fourier sense. Numerical experiments are carried out with typical testing problems to validate the effectiveness of the new algorithms.

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Acknowledgments

The authors would like to thank the anonymous referees for their time spent and extremely valuable remarks given. Their suggestions have significantly improved the quality and presentation of this paper. The last author appreciates particularly the M3HPCST-2020 conference and its organizers. Last but not least, the authors would also thank the editor for the tremendous amount of encouragement received throughout the preparation of this article.

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Authors and Affiliations

  1. Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China

    Chun-Hua Zhang & Hai-Wei Sun

  2. Key Laboratory of Grain Information Processing and Control, Ministry of Education of China, and College of Information Science and Engineering, Henan University of Technology, Zhengzhou, 450001, China

    Jun-Wei Jin

  3. Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, TX, 76798-7328, USA

    Qin Sheng

Authors
  1. Chun-Hua Zhang
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  2. Jun-Wei Jin
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  3. Hai-Wei Sun
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  4. Qin Sheng
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Corresponding author

Correspondence to Qin Sheng.

Additional information

The first three authors are supported in part by the Science and Technology Development Fund and University of Macau, Macau, through Research Grants (No. 0118/2018/A3) and (MYRG2018-00015-FST). The last author is supported in part by a Research Award from the CAS, Baylor University, USA.

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Zhang, CH., Jin, JW., Sun, HW. et al. A Spatially Sixth-Order Hybrid L1-CCD Method for Solving Time Fractional Schrödinger Equations. Appl Math 66, 213–232 (2021). https://doi.org/10.21136/AM.2020.0339-19

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