Time second‐order splitting conservative difference scheme for nonlinear fractional Schrödinger equation
Time second‐order splitting conservative difference scheme for nonlinear fractional Schrödinger equation
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DOI：
10.1002/mma.8790
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发表时间：
2022-10
影响因子：
2.9
通讯作者：
Jianqiang Xie;M. Ali;Zhiyue Zhang
中科院分区：
文献类型：
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作者：
Jianqiang Xie;M. Ali;Zhiyue Zhang
本文对高维非线性分数阶Schrödinger方程的新型时间二阶分裂保守有限差分法进行了严格的误差估计。证明了该方案的离散保存特性。利用截断技术和离散能量法，我们的方案在L2范数意义上具有O（Δt2+hx2+hy2）的精度。数值实验验证了该方法的准确性和守恒性。
This paper concentrates on the error estimation of novel time second‐order splitting conservative finite difference method (FDM) for high‐dimensional nonlinear fractional Schrödinger equation rigorously. The discrete preservation property of our scheme is exhibited. By virtue of the cut‐off technique and discrete energy method, it is shown that our scheme possesses the accuracy of O(Δt2+hx2+hy2) in sense of L2 ‐ norm. Numerical experiments are exhibited to validate the accuracy and conservation property of our scheme.