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Compact Discrete Gradient Schemes for Nonlinear Schrödinger Equations

  • Xiuling Yin EMAIL logo , Chengjian Zhang EMAIL logo and Jingjing Zhang
Published/Copyright: January 19, 2017

Abstract

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.

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

Funding statement: 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.

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Received: 2014-5-29
Accepted: 2016-12-14
Published Online: 2017-1-19
Published in Print: 2017-2-1

©2017 by De Gruyter

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