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Space-time finite element method for schrödinger equation and its conservation

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Abstract

Energy conservation of nonlinear Schrödinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrödinger partial equation. The numerical results are in accordance with the theory.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, P. R. China

    Tang Qiong  (汤琼) (Associate Professor, Doctor) & Chen Chuan-miao  (陈传淼)

  2. Department of Information and Mathematics Science, Zhuzhou Institute of Technology, Zhuzhou, 412008, Hunan Province, P. R. China

    Tang Qiong  (汤琼) (Associate Professor, Doctor) & Liu Luo-hua  (刘罗华)

Authors
  1. Tang Qiong  (汤琼)
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  2. Chen Chuan-miao  (陈传淼)
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  3. Liu Luo-hua  (刘罗华)
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Corresponding author

Correspondence to Tang Qiong  (汤琼).

Additional information

Communicated by LÜ He-xiang

Project supported by the National Basic Research Program of China (973 program) (No.G1999032804)

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Tang, Q., Chen, Cm. & Liu, Lh. Space-time finite element method for schrödinger equation and its conservation. Appl Math Mech 27, 335–340 (2006). https://doi.org/10.1007/s10483-006-0308-z

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  • DOI: https://doi.org/10.1007/s10483-006-0308-z

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2000 Mathematics Subject Classification

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