论文标题
连续无序的非线性schrödinger方程的数值集成符
Numerical integrators for continuous disordered nonlinear Schrödinger equation
论文作者
论文摘要
在本文中，我们考虑了连续无序的非线性schrödinger方程的数值解，该方程包含空间随机势。我们在此问题上解决了通常的数值集成商的有限时间准确性降低问题，这是由于存在随机/粗糙的潜力。通过使用（33，Siam J.Numer。Anal。，2019）的最近提出的低规度积分器（LRI），我们通过丢失两个空间衍生物来展示如何整合潜在项。进行融合分析是为了表明LRI具有$ h^2 $的潜力的$ l^2 $ norm中的第二阶准确度。进行数值实验以验证这一理论结果。提出了更多的数值结果，以研究LRI的准确性，而在应用程序中更粗糙的随机电位下，经典方法的准确性。
In this paper, we consider the numerical solution of the continuous disordered nonlinear Schrödinger equation, which contains a spatial random potential. We address the finite time accuracy order reduction issue of the usual numerical integrators on this problem, which is due to the presence of the random/rough potential. By using the recently proposed low-regularity integrator (LRI) from (33, SIAM J. Numer. Anal., 2019), we show how to integrate the potential term by losing two spatial derivatives. Convergence analysis is done to show that LRI has the second order accuracy in $L^2$-norm for potentials in $H^2$. Numerical experiments are done to verify this theoretical result. More numerical results are presented to investigate the accuracy of LRI compared with classical methods under rougher random potentials from applications.
