Convergence analysis of a symplectic semi-discretization for stochastic NLS equation with quadratic potential

2017/04/05 by Jialin Hong, Hong, Jialin, Liying Zhang +2
Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Physics Problems #FOS: Mathematics #Financial Markets and Investment Strategies #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1704.01268

openalex publication_date 2017/04/05 · openalex created_date 2018/04/13 · openalex updated_date 2026/08/01

Abstract

In this paper, we investigate the convergence in probability of a stochastic symplectic scheme for stochastic nonlinear Schrödinger equation with quadratic potential and an additive noise. Theoretical analysis shows that our symplectic semi-discretization is of order one in probability under appropriate regularity conditions for the initial value and noise. Numerical experiments are given to simulate the long time behavior of the discrete average charge and energy as well as the influence of the external potential and noise, and to test the convergence order.

Related

• Symplectic Runge-Kutta Semi-discretization for Stochastic Schrödinger Equation
• Stochastic Symplectic and Multi-Symplectic Methods for Nonlinear Schrödinger Equation with White Noise Dispersion
• Convergence in probability of an ergodic and conformal multi-symplectic numerical scheme for a damped stochastic NLS equation
• Numerical Analysis on Ergodic Limit of Approximations for Stochastic NLS Equation via Multi-symplectic Scheme
• Low regularity symplectic schemes for stochastic NLS