An unconditionally stable linearized CCD–ADI method forgeneralized nonlinear Schrödinger equations with variable coefficients in two and three dimensions
An unconditionally stable linearized CCD–ADI method forgeneralized nonlinear Schrödinger equations with variable coefficients in two and three dimensions
复制标题
用于二维和三维可变系数广义非线性薛定谔方程的无条件稳定线性化 CCD-ADI 方法
DOI：
10.1016/j.camwa.2017.04.009
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发表时间：
2017
影响因子：
2.9
通讯作者：
Pan Kejia
中科院分区：
文献类型：
--
作者：
He Dongdong;Pan Kejia
本文提出了求解二维和三维变系数广义非线性薛定谔方程的三层线性隐式组合紧致差分法和交替方向隐式方法。该方法对空间变量具有六阶精度，对时间变量具有二阶精度。傅立叶分析表明，该方法是无条件稳定的。与求解二维常系数三次非线性最小二乘问题的非线性CCD-PRADI格式(Li et al.，2015)相比，目前的方法是一种线性格式，通常所需的计算量要小得多。此外，目前的方法可以自然地处理变系数三维问题。最后，给出了二维和三维情况下的数值结果，说明了该方法的优越性。
In this paper, we propose a three-level linearly implicit combined compact difference method (CCD) together with alternating direction implicit method (ADI) for solving the generalized nonlinear Schrödinger equation (NLSE) with variable coefficients in two and three dimensions. The method is sixth-order accurate in space variable and second-order accurate in time variable. Fourier analysis shows that the method is unconditionally stable. Comparing to the nonlinear CCD–PRADI scheme for solving the 2D cubic NLSE with constant coefficients (Li et al., 2015), current method is a linear scheme which generally requires much less computational cost. Moreover, current method can handle 3D problems with variable coefficients naturally. Finally, numerical results for both 2D and 3D cases are presented to illustrate the advantages of the proposed method.