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Second-Order SAV Schemes for the Nonlinear Schrödinger Equation and Their Error Analysis

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Abstract

We consider a second-order SAV scheme for the nonlinear Schrödinger equation in the whole space with typical generalized nonlinearities, and carry out a rigorous error analysis. We also develop a fully discretized SAV scheme with Hermite–Galerkin approximation for the space variables, and present numerical experiments to validate our theoretical results.

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Funding

The work of J. Shen is supported in part by NSF Grant DMS-2012585 and by AFOSR FA9550-20-1-0309. The work of Q. Zhuang is supported in part by National Natural Science Foundation of China (No. 11771083), and the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University(No. ZQN-702). Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, 47907, IN, USA

    Beichuan Deng & Jie Shen

  2. Fujian Province University Key Laboratory of Computation Science, School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    Qingqu Zhuang

Authors
  1. Beichuan Deng
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  2. Jie Shen
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  3. Qingqu Zhuang
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Correspondence to Jie Shen.

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Deng, B., Shen, J. & Zhuang, Q. Second-Order SAV Schemes for the Nonlinear Schrödinger Equation and Their Error Analysis. J Sci Comput 88, 69 (2021). https://doi.org/10.1007/s10915-021-01576-y

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  • DOI: https://doi.org/10.1007/s10915-021-01576-y

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