分数阶Klein-Gordon-Schrodinger方程的保能量方法  

The Energy-Preserving Method for the Fractional Klein-Gordon-Schrodinger Equation

作　　者：张利娟 孙建强 ZHANG Lijuan;SUN Jianqiang(College of Science,Hainan University,Haikou Hainan 570228,China)

机构地区：[1]海南大学理学院,海南海口570228

出　　处：《江西师范大学学报（自然科学版）》2022年第3期257-261,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11961020)资助项目。

摘　　要：该文先将分数阶Klein-Gordon-Schrodinger方程转化成辛结构的哈密尔顿系统,利用傅里叶拟谱方法对Riesz空间分数阶导数进行近似离散,得到分数阶Klein-Gordon-Schrodinger方程有限维哈密尔顿系统;再利用2阶平均向量场方法对有限维哈密尔顿系统离散,得到分数阶Klein-Gordon-Schrodinger方程新的保能量格式;最后利用新的保能量格式数值模拟方程孤立波的演化行为,并分析新格式的保能量守恒特性.The fractional Klein-Gordon-Schrodinger equation are transformed into the Hamiltonian system with the symplectic structure.The Riesz space-fractional derivation is discretized approximately by the Fourier pseudo-pectral method.The finite dimensional Hamiltonian system of the fractional Klein-Gordon-Schrodinger equation is obtained.The second order average vector field method is applied to solve the finite dimensional Hamiltonian system.The new energy preserving scheme of the fractional Klein-Gordon-Schrodinger equation is obtained.The new scheme is applied to numerically simulate the solitary evolution behaviors of the equation, moreover the energy conservation property of the new scheme is investigated.

关 键 词：平均向量场方法 分数阶Klein-Gordon-Schrodinger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]