Mass- and energy-conserving difference schemes for nonlinear fractional Schrodinger equations
Mass- and energy-conserving difference schemes for nonlinear fractional Schrodinger equations
复制标题
非线性分数阶薛定谔方程的质量和能量守恒差分格式
DOI：
10.1016/j.aml.2020.106686
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发表时间：
2021
影响因子：
3.7
通讯作者：
Li Dongfang
中科院分区：
文献类型：
--
作者：
Li Xiaoxi;Wen Jinming;Li Dongfang
本文对非线性分数阶薛定谔方程提出了一种全离散的保结构格式。关键是引入标量辅助变量，并将方程重写为一族新的系统。采用隐式中点法、迭代梯形法和分数中心差分法对新系统进行了逼近。结果表明，全离散格式是质量守恒和能量守恒的。这与以前的结果形成了鲜明对比，即全离散格式只对原始方程是质量守恒的。
In this paper, we present a fully discrete and structure-preserving scheme for the nonlinear fractional Schrödinger equations. The key is to introduce a scalar auxiliary variable and rewrite the equations as a new family of systems. The new systems are approximated by using the implicit midpoint rule, the repeated trapezoidal rule and the fractional centered difference method. It is shown the fully discrete scheme is mass- and energy-conserved. This is sharp contrast to the former result, i.e., the fully discrete scheme is only mass-conserved for the original equations.