TY - JOUR
T1 - Strong convergence rate of splitting schemes for stochastic nonlinear Schrödinger equations
AU - Cui, Jianbo
AU - Hong, Jialin
AU - Liu, Zhihui
AU - Zhou, Weien
N1 - Funding Information:
This work was supported by National Natural Science Foundation of China (NO. 91530118, NO. 91130003, NO. 11021101, NO. 91630312 and NO. 11290142).
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/4/15
Y1 - 2019/4/15
N2 - In this paper, we show that solutions of stochastic nonlinear Schrödinger (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 +τ [Formula presented] ) of the spectral splitting Crank–Nicolson scheme, where N and τ denote the dimension of the approximate space and the time step size, respectively.
AB - In this paper, we show that solutions of stochastic nonlinear Schrödinger (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 +τ [Formula presented] ) of the spectral splitting Crank–Nicolson scheme, where N and τ denote the dimension of the approximate space and the time step size, respectively.
KW - Exponential integrability
KW - Non-monotone coefficients
KW - Splitting scheme
KW - Stochastic nonlinear Schrödinger equation
KW - Strong convergence rate
UR - http://www.scopus.com/inward/record.url?scp=85054444033&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2018.10.034
DO - 10.1016/j.jde.2018.10.034
M3 - Journal article
AN - SCOPUS:85054444033
SN - 0022-0396
VL - 266
SP - 5625
EP - 5663
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 9
ER -