分数阶Klein-Gordon-Zakharov方程新的保能量格式  

New Energy Preserving Scheme of Fractional Klein-Gordon-Zakharov Equations

作　　者：王昌琳 刘莹 孙建强 Wang Changlin;Liu Ying;Sun Jianqiang(College of Science,Hainan University,Haikou 570228,China)

机构地区：[1]海南大学理学院,海南海口570228

出　　处：《海南大学学报（自然科学版）》2021年第4期318-324,共7页Natural Science Journal of Hainan University

基　　金：国家自然科学基金(11961020)。

摘　　要：将分数阶Klein-Gordon-Zakharov方程转化成多辛结构的偏微分方程,利用傅里叶拟谱方法对方程Riesz空间分数阶导数进行近似离散,得到有限维的常微分方程组,再利用二阶平均向量场方法对常微分方程组离散,得到方程新的保能量格式,最后利用新格式数值模拟分数阶Klein-Gordon-Zakharov方程孤立波的演化行为并分析格式的保能量守恒特性.In the report,the fractional Klein-Gordon-Zakharovs were transformed into the multi-symplectic structure partial differential equations,the Fourier pseudo method was used for the approximatediscretization of the spacefractional derivative of the Riesz equation,an ordinary differential equations were obtained.The second order average vector field method was used for the discretization of the ordinary differential equations,a new energy preserving scheme of the equation was obtained.The new scheme was used to simulate the solitary wave behaviors of the fractional Klein-Gordon-Zakharovs equations,and the energy conservation property of the new scheme was analyzed.

关 键 词：二阶平均向量方法 分数阶Klein-Gordon-Zakharov方程 傅里叶拟谱方法 能量守恒格式 

分 类 号：O241.5[理学—计算数学]