Volume 12, Issue 1
Convergence Analysis on Stochastic Collocation Methods for the Linear Schrodinger Equation with Random Inputs

Zhizhang Wu and Zhongyi Huang

10.4208/aamm.OA-2019-0008

Adv. Appl. Math. Mech., 12 (2020), pp. 30-56.

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  • Abstract

In this paper, we analyse the stochastic collocation method for a linear Schrodinger 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.

  • History

Published online: 2019-12

  • AMS Subject Headings

65M12, 81Q05, 60H25

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