TY - JOUR
T1 - Analysis of a splitting scheme for damped stochastic nonlinear Schrödinger equation with multiplicative noise
AU - Cui, Jianbo
AU - Hong, Jialin
N1 - Funding Information:
∗Received by the editors November 1, 2017; accepted for publication (in revised form) April 16, 2018; published electronically July 10, 2018. http://www.siam.org/journals/sinum/56-4/M115490.html Funding: This work was supported by National Natural Science Foundation of China (91630312, 91530118, and 11290142). †Corresponding author. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China ([email protected]). ‡School of Mathematical Science, University of Chinese Academy of Sciences, Beijing, 100049, China ([email protected]).
Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.
PY - 2018/7/10
Y1 - 2018/7/10
N2 - In this paper, we investigate the damped stochastic nonlinear Schrödinger (NLS) equation with multiplicative noise and its splitting-based approximation. When the damped effect is large enough, we prove that the solutions of both the damped stochastic NLS equation and the splitting scheme are exponentially stable and possess some exponential integrability. These properties show that the strong order of the scheme is 1 2 and independent of time. Additionally, we analyze the regularity of the Kolmogorov equation with respect to the stochastic NLS equation. As a consequence, the weak order of the scheme is shown to be 1 and independent of time.
AB - In this paper, we investigate the damped stochastic nonlinear Schrödinger (NLS) equation with multiplicative noise and its splitting-based approximation. When the damped effect is large enough, we prove that the solutions of both the damped stochastic NLS equation and the splitting scheme are exponentially stable and possess some exponential integrability. These properties show that the strong order of the scheme is 1 2 and independent of time. Additionally, we analyze the regularity of the Kolmogorov equation with respect to the stochastic NLS equation. As a consequence, the weak order of the scheme is shown to be 1 and independent of time.
KW - Damped stochastic nonlinear Schrödinger equation
KW - Exponential integrability
KW - Kolmogorov equation
KW - Strong order
KW - Weak order
UR - http://www.scopus.com/inward/record.url?scp=85053549006&partnerID=8YFLogxK
U2 - 10.1137/17M1154904
DO - 10.1137/17M1154904
M3 - Journal article
AN - SCOPUS:85053549006
SN - 0036-1429
VL - 56
SP - 2045
EP - 2069
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 4
ER -