In this paper, we design two classes of high-accuracy conservative numerical algorithms for the nonlinear Klein-Gordon-Schrödinger system in two dimensions. By introducing the energy quadratization technique, we first transform the original system into an equivalent one, where the energy is modified as a quadratic form. The Gauss-type Runge-Kutta method and the Fourier pseudo-spectral method are then employed to discretize the reformulation system in time and space, respectively. The fully discrete schemes inherit the conservation of mass and modified energy and can reach high-order accuracy in both temporal and spatial directions. In order to complement the proposed schemes and speed up the calculation, we also develop another class of conservative schemes combined with the prediction-correction technique. Numerous experimental results are reported to demonstrate the efficiency and high accuracy of the new methods.

在本文中，我们为二维非线性 Klein-Gordon-Schrödinger 系统设计了两类高精度保守数值算法。通过引入能量二次化技术，我们首先将原始系统转换为等效系统，其中能量被修改为二次形式。然后采用高斯型龙格-库塔法和傅里叶伪谱法分别在时间和空间上对重构系统进行离散化。完全离散方案继承了质量守恒和修正能量守恒，在时间和空间方向上都可以达到高阶精度。为了补充所提出的方案并加快计算速度，我们还开发了另一类结合预测校正技术的保守方案。