Conservative compact difference scheme for the Zakharov–Rubenchik equations

ABSTRACT

In this article, a compact difference scheme is investigated to solve the Zakharov–Rubenchik equations in one dimension. The new scheme is proved to conserve the total mass and energy in the discrete sense. Rigorous error estimates are established for the new method with the help of an induction argument in energy space which show that the new scheme has second-order accuracy in time and fourth-order accuracy in space. Extensive numerical results are provided to verify our theoretical analysis, and show the accuracy and efficiency of the new scheme.

Keywords:

• Zakharov–Rubenchik equations
• induction argument
• compact difference scheme
• conservation laws
• convergence

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M06
• 35Q51

Acknowledgments

The authors would like to express sincere appreciation to the anonymous reviewers for their comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number: 11571181].