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文章摘要
孔嘉萌,孙建强,袭春晓.sine-Gordon方程新的保能量格式[J].海南大学学报编辑部:自然科学版,2018,36(4):.
sine-Gordon方程新的保能量格式
New Energy-Preserving Scheme of sine-Gordon Equation
投稿时间:2018-07-06  修订日期:2018-10-09
DOI:
中文关键词: 多辛整体保能量方法;平均向量场方法;Boole离散线积分法;sine-Gordon方程
英文关键词: Multi-symplectic global energy-preserving method;Average vector field method;Boole discrete line integral method;sine-Gordon equation
基金项目:国家自然科学基金地区科学基金
作者单位E-mail
孔嘉萌 海南大学 18463756744@163.com 
孙建强 海南大学 sunjq123@qq.com 
袭春晓 海南大学  
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中文摘要:
      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.新格式应用于数值模拟能量守恒的一维多辛sine-Gordon方程. 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,且很好地保持了孤立波的能量守恒特性. 新格式有效地消除了sine-Gordon方程中正弦函数产生的奇异积分.新格式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.
英文摘要:
      The integral term of the multi-symplectic global energy-preserving scheme is discretizated by the Boole discrete line integral method. A new multi-symplectic global energy-preserving scheme is obtained. The new scheme is applied to numerically simulate the one dimensional sine-Gordon equation. Numerical results show that the new scheme can well simulate the behaviors of the sine-Gordon equation with the different initial conditions, moreover 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. The new scheme has important meaning in numerically simulating the complex energy conserving multi-symplectic structure partial differential equation.
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