Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 266, Issue 9, Pages 5625-5663Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2018.10.034
Keywords
Stochastic nonlinear Schrodinger equation; Strong convergence rate; Exponential integrability; Splitting scheme; Non-monotone coefficients
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Funding
- National Natural Science Foundation of China [91530118, 91130003, 11021101, 91630312, 11290142]
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In this paper, we show that solutions of stochastic nonlinear Schrodinger (NLS) equations can be approximated by solutions of coupled splitting systems. Based on these systems, we propose a new kind of fully discrete splitting schemes which possess algebraic strong convergence rates for stochastic NLS equations. Key ingredients of our approach are using the exponential integrability and stability of the corresponding splitting systems and numerical approximations. In particular, under very mild conditions, we derive the optimal strong convergence rate O(N-2 + tau(1/2)) of the spectral splitting Crank-Nicolson scheme, where N and tau denote the dimension of the approximate space and the time step size, respectively. (C) 2018 Elsevier Inc. All rights reserved.
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