求解耦合非线性Klein-Gordon-Schrödinger方程的能量稳定方法

Energy Stable Method for Coupled Nonlinear Klein-Gordon-Schrödinger Equation

研究基于指数标量辅助变量方法的耦合非线性Klein-Gordon-Schrödinger方程有效数值方法.首先,采用指数标量辅助变量处理方程的非线性项,构造求解方程的无条件能量稳定格式;然后,对方程在时间方向上采用Crank-Nicolson格式进行离散,在空间方向上采用紧致差分格式进行离散,证明全离散格式的修正能量守恒律.最后,通过数值算例进行验证.结果表明:文中格式具有有效性,修正能量具有守恒性.

The efficient numerical method of coupled nonlinear Klein-Gordon-Schr dinger equation based on exponential scalar auxiliary variable method is studied.Firstly,the nonlinear terms of the equation are treated with exponential scalar auxiliary variables,and an unconditional energy stable scheme is constructed to the solution of the equation.Then,the equation is discretized by Crank-Nicolson scheme in time direction and by compact difference scheme in space direction,the modified energy conservation law of the full discrete scheme is proved.Finally,it is verified by numerical examples that the proposed scheme is effective and the modified energy is conserved.