sine-Gordon方程新的保能量格式

New Energy-Preserving Scheme of sine-Gordon Equation

首先利用Boole离散线积分法对多辛整体保能量格式中的积分项数值离散,得到一个新的多辛整体保能量格式,其次将新格式应用于数值模拟能量守恒的一维多辛sine-Gordon方程,最后数值结果表明,新格式能很好地模拟sine-Gordon方程在不同初值条件下孤立波的运动,较好地保持了孤立波的能量守恒特性,有效地消除了sine-Gordon方程中正弦函数产生的奇异积分,并在数值模拟复杂的能量守恒多辛结构偏微分方程中具有优越性.

In the report,the Boole discrete line integral method was used to discretizate the integral term of the multi-symplectic global energy-preserving scheme,and a new multi-symplectic global energy-preserving scheme was obtained. The new scheme was used for simulating the one dimensional sine-Gordon equation. The numerical results showed that the new scheme can well simulate the behaviors of the sine-Gordon equation with the different initial conditions,and preserve the energy conservation property of the solitary waves. The new scheme can avoid the singular integral of the sine function of the sine-Gordon equation effectively and has the important meaning in numerically simulating the complex energy conserving multi-symplectic structure partial differential equation.