Error estimates of exponential wave integrator sine pseudospectral method for Schrödinger–Boussinesq system

Abstract

In this article, an exponential wave integrator sine pseudospectral method is formulated and analysed for discretizing the coupled Schrödinger–Boussinesq system. Our method is based on the utilizations of sine pseudospectral discretization for spatial derivatives followed by exponential wave integrator for temporal derivatives in phase space. The scheme is fully explicit and very efficient due to discrete sine transform (DST), and it is of spectral accuracy in space and second-order accuracy in time. Numerical analysis of the proposed method is carried out and rigorous error estimates are established via discrete energy and induction argument method. The numerical results are reported to verify our theoretical analysis.

Keywords:

• Schrödinger–Boussinesq system
• exponential wave integrator
• DST
• Parserval's identity
• inverse inequality
• error estimates

2010 Mathematics Subject Classifications:

• 65M70
• 65T40

Acknowledgments

The authors wish to thank the anonymous referees for their hard work and valuable comments. This work is supported by the National Natural Science Foundation of China under Grant No.11571181 and Changshu Institute of Technology Talent Introduction Project under Grant No. KYZ2018033Q.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors wish to thank the anonymous referees for their hard work and valuable comments. This work is supported by the National Natural Science Foundation of China [grant number 11571181] and Changshu Institute of Technology Talent Introduction Project under Grant No. KYZ2018033Q.