High-Order Operator-Compensation Schemes with Mass and Energy Conservation for the Multi-Dimensional Zakharov System

This paper presents high-order operator-compensation (OC) methods and the Crank-Nicolson (CN) technology to solve the Zakharov system (ZS). Firstly, the OC method is used for spatial discretization, and semi-discrete high-order OC schemes are obtained, which can maintain mass and energy conservation. Subsequently, the CN technology is adopted for temporal discretization, and full-discrete high-order OC schemes are obtained, which can inherit mass and energy conservation and achieve arbitrary even-order accuracy in space and second-order accuracy in time. In the process of solving ZS, we employ the linearization method to handle the nonlinear ZS, which significantly improves the computational efficiency. Considering the large stencil of numerical schemes, we propose a fast numerical iterative method to deal with the problem, which saves the computational cost. Numerical experiments are given to test accuracy order, verify conservation property, and simulate dynamic evolution.