A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations
A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations
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DOI：
10.1016/j.jcp.2014.04.047
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
Dongling Wang;A. Xiao;Wei Yang
中科院分区：
文献类型：
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作者：
Dongling Wang;A. Xiao;Wei Yang
本文对具有分数阶导数的耦合非线性薛定谔方程组提出了一种线性隐式守恒差分格式。该方案在离散水平上保持了质量和能量守恒，每一步只需求解一个线性方程组。证明了差分解的存在唯一性。讨论了该格式的稳定性和收敛性，证明了在离散l2模下，随着时间步长τ和网格尺寸h，该格式具有O（τ 2+ h2）阶收敛性。当分数阶数为2时，所得结果与经典非分数阶耦合非线性薛定谔方程的差分格式雅阁.文中还给出了一些数值算例。
In this paper, a linearly implicit conservative difference scheme for the coupled nonlinear Schrödinger equations with space fractional derivative is proposed. This scheme conserves the mass and energy in the discrete level and only needs to solve a linear system at each step. The existence and uniqueness of the difference solution are proved. The stability and convergence of the scheme are discussed, and it is shown to be convergent of order O (τ 2+ h 2) in the discrete l 2 norm with the time step τ and mesh size h. When the fractional order is two, all those results are in accord with the difference scheme proposed for the classical non-fractional coupled nonlinear Schrödinger equations. Some numerical examples are also reported.