Convergence Analysis on Stochastic Collocation Methods for the Linear Schrödinger Equation with Random Inputs
Year: 2020
Author: Zhizhang Wu, Zhongyi Huang
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 30–56
Abstract
In this paper, we analyse the stochastic collocation method for a linear Schrödinger equation with random inputs, where the randomness appears in the potential and initial data and is assumed to be dependent on a random variable. We focus on the convergence rate with respect to the number of collocation points. Based on the interpolation theories, the convergence rate depends on the regularity of the solution with respect to the random variable. Hence, we investigate the dependence of the stochastic regularity of the solution on that of the random potential and initial data. We provide sufficient conditions on the random potential and initial data to ensure the smoothness of the solution and the spectral convergence. Finally, numerical results are presented to support our analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0008
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 30–56
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Schrödinger equation stochastic collocation methods convergence analysis uncertainty quantification.