A conservative compact difference scheme for the Zakharov equations in one space dimension

ABSTRACT

In this paper, we present a conservative fourth-order compact difference scheme for the initial-boundary value problem of the Zakharov equations. Discrete conservation laws, convergence and stability of the new scheme are proved by energy method. Several numerical results are reported to support our theoretical analysis.

Keywords:

• Zakharov equations
• compact difference scheme
• discrete conservation laws
• convergence
• stability

2010 AMS Subject Classification:

• 65M06

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Ordinary University Graduate Student Research Innovation Projects of Jiangsu Province (2015) [grant number KYZZ15_0089].