63 citations · 585 across the 80 of their papers we have counts for
9 papers · 1 filter
Convergence in probability of an ergodic and conformal multi-symplectic numerical scheme for a damped stochastic NLS equation
Jialin Hong, Lihai Ji, Xu Wang
In this paper, we investigate the convergence order in probability of a novel ergodic numerical scheme for damped stochastic nonlinear Schrödinger equation with an additive noise.…
Optimal Error Estimates of Conservative Local Discontinuous Galerkin Method for Nonlinear Schrödinger Equation
Jialin Hong, Lihai Ji, Zhihui Liu
In this paper, we propose a conservative local discontinuous Galerkin method for one-dimensional nonlinear Schrödinger equation. By using special upwind-biased numerical fluxes, we…
Strong Convergence Rate of Finite Difference Approximations for Stochastic Cubic Schrödinger Equations
Jianbo Cui, Jialin Hong, Zhihui Liu
In this paper, we derive a strong convergence rate of spatial finite difference approximations for both focusing and defocusing stochastic cubic Schrödinger equations driven by a m…
Optimal Hölder Continuity and Hitting Probabilities for SPDEs with Rough Fractional Noises
Jialin Hong, Zhihui Liu, Derui Sheng
We investigate the optimal Hölder continuity and hitting probabilities for systems of stochastic heat equations and stochastic wave equations driven by an additive fractional Brown…
Stochastic Symplectic and Multi-Symplectic Methods for Nonlinear Schrödinger Equation with White Noise Dispersion
Jianbo Cui, Jialin Hong, Zhihui Liu +1
We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propo…
Numerical Analysis on Ergodic Limit of Approximations for Stochastic NLS Equation via Multi-symplectic Scheme
Jialin Hong, Xu Wang, Liying Zhang
We consider a finite dimensional approximation of the stochastic nonlinear Schrödinger equation driven by multiplicative noise, which is derived by applying a symplectic method to…
Projection methods for stochastic differential equations with conserved quantities
Weien Zhou, Liying Zhang, Jialin Hong +1
In this paper, we consider the numerical methods preserving single or multiple conserved quantities, and these methods are able to reach high order of strong convergence simultaneo…
Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise
Weien Zhou, Jingjing Zhang, Jialin Hong +1
In this paper, we construct stochastic symplectic Runge--Kutta (SSRK) methods of high strong order for Hamiltonian systems with additive noise. By means of colored rooted tree theo…
Approximating Stochastic Evolution Equations with Additive White and Rough Noises
Yanzhao Cao, Jialin Hong, Zhihui Liu
In this paper, we analyze Galerkin approximations for stochastic evolution equations driven by an additive Gaussian noise which is temporally white and spatially fractional with Hu…