High-order conservative energy quadratization schemes for the Klein-Gordon-Schrodinger equation

作者：Li, Xin^*; Zhang, Luming

来源：ADVANCES IN COMPUTATIONAL MATHEMATICS, 2022, 48(4): 41.

DOI：10.1007/s10444-022-09962-2

• Klein-Gordon-Schrodinger equation
• Energy quadratization
• Gauss-type Runge-Kutta method
• Fourier pseudo-spectral method
• Prediction-correction
• Conservation
• 65Mxx

In this paper, we design two classes of high-accuracy conservative numerical algorithms for the nonlinear Klein-Gordon-Schrodinger 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.

• 单位
  南京航空航天大学