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Unconditional convergence and optimal error estimates of the Euler semi-implicit scheme for a generalized nonlinear Schrödinger equation

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Abstract

In this paper, we focus on a linearized backward Euler scheme with a Galerkin finite element approximation for the time-dependent nonlinear Schrödinger equation. By splitting an error estimate into two parts, one from the spatial discretization and the other from the temporal discretization, we obtain unconditionally optimal error estimates of the fully-discrete backward Euler method for a generalized nonlinear Schrödinger equation. Numerical results are provided to support our theoretical analysis and efficiency of this method.

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Authors and Affiliations

  1. Center for Computational Geosciences, School of Mathematics and Statistics, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an, Shaanxi, 710049, People’s Republic of China

    Wentao Cai & Zhangxin Chen

  2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013, People’s Republic of China

    Jian Li

  3. Department of Chemical and Petroleum Engineering, Schulich School of Engineer, University of Calgary, Calgary, AB, T2N 1N4, Canada

    Zhangxin Chen

Authors
  1. Wentao Cai
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  2. Jian Li
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  3. Zhangxin Chen
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Correspondence to Zhangxin Chen.

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Communicated by: Raymond H. Chan

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Cai, W., Li, J. & Chen, Z. Unconditional convergence and optimal error estimates of the Euler semi-implicit scheme for a generalized nonlinear Schrödinger equation. Adv Comput Math 42, 1311–1330 (2016). https://doi.org/10.1007/s10444-016-9463-2

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  • DOI: https://doi.org/10.1007/s10444-016-9463-2

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