Energy-Preserving AVF Methods for Riesz Space-Fractional Nonlinear KGZ and KGS Equations
Energy-Preserving AVF Methods for Riesz Space-Fractional Nonlinear KGZ and KGS Equations
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DOI：
10.3390/fractalfract7100711
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发表时间：
2023-09
影响因子：
5.4
通讯作者：
Jianqiang Sun;Siqi Yang;Lijuan Zhang
中科院分区：
文献类型：
--
作者：
Jianqiang Sun;Siqi Yang;Lijuan Zhang
利用傅里叶伪谱方法对Riesz空间分数阶导数进行离散化。将Riesz空间分数阶非线性Klein-Gordon-Zakharov(KGZ)方程和Klein-Gordon-Schrödinger(KGS)方程转化为两个无限维哈密顿系统，并用FPS方法进行离散。由此得到两个有限维哈密顿系统，并用二阶平均矢量场(AVF)方法进行求解。证明了这些新的分数阶KGZ方程和KGS方程离散格式的能量守恒性。应用这些格式模拟了两个分数阶微分方程组的演化过程。数值结果表明，这些格式能够很好地模拟这些分数阶微分方程组的演化过程，并且保持了能量守恒的性质。
The Riesz space-fractional derivative is discretized by the Fourier pseudo-spectral (FPS) method. The Riesz space-fractional nonlinear Klein–Gordon–Zakharov (KGZ) and Klein–Gordon–Schrödinger (KGS) equations are transformed into two infinite-dimensional Hamiltonian systems, which are discretized by the FPS method. Two finite-dimensional Hamiltonian systems are thus obtained and solved by the second-order average vector field (AVF) method. The energy conservation property of these new discrete schemes of the fractional KGZ and KGS equations is proven. These schemes are applied to simulate the evolution of two fractional differential equations. Numerical results show that these schemes can simulate the evolution of these fractional differential equations well and maintain the energy-preserving property.