Analysis of A Splitting Scheme for Damped Stochastic Nonlinear Schr\'odinger Equation with Multiplicative Noise

Autor:	Cui, Jianbo, Hong, Jialin
Rok vydání:	2017
Předmět:	Mathematics - Numerical Analysis 60H35 35Q55 60H15 65M12
Druh dokumentu:	Working Paper
Popis:	In this paper, we investigate the damped stochastic nonlinear Schr\"odinger(NLS) equation with multiplicative noise and its splitting-based approximation. When the damped effect is large enough, we prove that the solutions of the damped stochastic NLS equation and the splitting scheme are exponential stable and possess some exponential integrability. These properties lead that the strong order of the scheme is $\frac 12$ and independent of time. Meanwhile, we analyze the regularity of the Kolmogorov equation with respect to the equation. As a consequence, the weak order of the scheme is shown to be twice the strong order and independent of time. Comment: 24 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1711.00516 Zobrazit plný text záznamu View this record from Arxiv