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International Journal of Nonlinear Sciences and Numerical Simulation

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Volume 18, Issue 1 (Feb 2017)


Compact Discrete Gradient Schemes for Nonlinear Schrödinger Equations

Xiuling Yin
  • Corresponding author
  • School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • School of mathematical sciences, Dezhou University, Dezhou 253023, China
  • Email:
/ Chengjian Zhang
  • Corresponding author
  • School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • Email:
/ Jingjing Zhang
  • School of Science, East China Jiaotong University, Nanchang 330013, Jiangxi, China
Published Online: 2017-01-19 | DOI: https://doi.org/10.1515/ijnsns-2014-0064


This paper proposes two schemes for a nonlinear Schrödinger equation with four-order spacial derivative by using compact scheme and discrete gradient methods. They are of fourth-order accuracy in space. We analyze two discrete invariants of the schemes. The numerical experiments are implemented to investigate the efficiency of the schemes.

Keywords: Schrödinger equation; compact scheme; discrete gradient method; discrete invariant

MSC 2010: 65M06; 65M12; 65Z05; 70H15


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About the article

Received: 2014-05-29

Accepted: 2016-12-14

Published Online: 2017-01-19

Published in Print: 2017-02-01

The authors are supported by the Director Innovation Foundation of ICMSEC and AMSS, the Foundation of CAS, the NNSFC (Nos. 11571128, 11501082, 11201125) and the NSF of Shandong Province (Nos. ZR2015AL016, ZR2016AQ07). The authors would like to thank the referees for valuable suggestions.

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2014-0064. Export Citation

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