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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.
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].